In this course statistical methods for scientists and engineers, I plan to cover several topics which are of one of the you can say most important topics for practicing scientists and engineers. So, let me just say few of these terms here, we will be introducing the term probability and we talked about random variables and probability distributions. Then we discuss the main statistical methods that is of a parametric point estimation and testing of hypothesis. We will introduce one of the most widely applicable methodologies that is known as fitting of linear models under the term regression analysis. In planning of the experiments, we consider experimental designs and we do the multivariate data analysis and lastly we will cover non-parametric methods. So, this is the outline of the course which will be available on the website also. Let me introduce the term probability. So, we start with the foundations of probability. Usually speaking we can say that the term probability is probably as old as the civilization itself, because people have been talking in terms like it is very likely that it will rain today. The winter seems to be colder than the last winter and it is likely to go progressively more cold in the next year. It is it looks as if or the chances are that the food production this year will be more than the last year. It is likely or there is a chance that the patient who is being operated will survive the operation. So, this type of sentences or terminology have been in use. However, and certainly it leads to the understanding that there is something called chance, probable, likely. However, a scientific study of probability theory started around 16th and 17th century in Europe during the renaissance period. And probably the first published work in this direction is by Huygens who whose duration was 1629 to 1695 and his published work in 1657 described the term probability and gave a possible explanation of various type of events for which the probabilities can be calculated. Let me point out that the formal study of probability started with the discussion of the gambling games. So, that time in the Europe the people who were involved in the betting, gambling, coin tossing, die throwing, casinos etcetera. They approached the mathematicians of the day to answer questions about that on which event they can bet so that their winnings will be more. And thus started famous correspondence with the two of the famous mathematicians of that day that is Fermat and Pascal. The timelines of Fermat is 1600 1 to 1657, 55 and Pascal lived from 1623 to 1662. In the correspondence between these two mathematicians the first formal discussions of probability theory were there and it slowly took root and especially the work by one of the Bernoulli that is James Bernoulli. And you can say that the first formal definition of the probability came in Laplace famous work in 1812 that is theory analytic dis probabilities. Later on his definition and approach was considered to be insufficient to answer many questions and therefore, the other approaches were introduced especially the empirical approach by Richard von Meisys. And finally, the mathematical firm mathematical definition that is by A. N. Kalmogorov Russian mathematician which was published in 1933. I will be briefly discussing these things in detail. So, let us consider that what is the basic terminology for probability and what makes us study the subject probability. So, in scientific theory we deal with experiments. So, we have experiments which we can classify into two parts for the purpose of this discussion into what is known as deterministic experiments. What are deterministic experiments? For example, I am holding this pen here and I put my pen on the paper then the outcome is that there is a ink flowing through it and it makes certain impression on the page. This is a deterministic experiment. If we switch on a bulb then the bulb lights up. If we open our mouth to speak then words come out and others can listen. If we consider experiments which are done in the classroom situations or in the laboratory situations many of the chemical experiments you mix two chemicals certain molecules of one chemical with the certain molecules of another chemical you get another molecule. You consider some genetic experiments you have genes of certain thing and you mix up with genes of another one you can use a gene for transplanting to treat a disease. So, these are the experiments which are of deterministic nature. That means, if we fix the conditions under which the experiment is performed the outcome is also fixed in advance. That means, it is known that what would be the outcome. For example, if we put a vessel full of water on a gas stove and we light the gas stove when the temperature of the water reaches 100 degree Celsius under a certain atmospheric pressure the outcome is that the water will boil. And similarly the boiling temperatures for various other commodities for example, milk tea or any other liquid is there. For example, you may even melt iron if you put it in a furnace with a very high temperature something like 1600 degree Celsius. These are examples of the deterministic experiments. However, in probability theory we are concerned with the experiments which are termed as random experiments. Now, what is it that separates random experiments from the deterministic experiments? As I mentioned in the deterministic experiments, if we fix the conditions under which the experiment is being conducted then the outcome is known in advance or it can be fixed in advance. However, there are other situations where even if we perform the experiment under fixed conditions, there are various other uncontrolled factors which make it impossible to predict the outcome of the experiment. So, for example, we study weather. So, weather is a subject which is studied by a physicist, meteorologist and so on. Even then every year what would be the average rainfall during the season, what will be the total rainfall during the season, what would be the total, what would be the average temperatures during a month. All of these things are varying that means, we cannot predict with certainty that this will be the thing. For example, we cannot say that during the monsoon season India Indian subcontinent or a particular town in a continent will get say 20 centimeter of the rain. We cannot say it with certainty, it may be it is 15 centimeter, it may be it is 30 centimeters and so on. A similar thing is about temperatures, a similar thing is true about say agricultural product. We may fix up a size of a farmland on which the seed of a certain crop will be sown. We may fix what kind of pesticides will be used, what type of fertilizer will be used, what with what frequency irrigation facilities will be provided and so on. Even then we cannot say that the total food grain production say wheat or rice or maize from that particular farmland would be say 100 metric ton or 50 metric ton or 10 metric ton etcetera. We cannot exactly say that how much would be the food grain production, it will be in certain range. We have a bulb. So, when we switch on the light I mean the light switch we have the outcome that the bulb will be lighting. However, what will be the total lifetime of the bulb that cannot be predicted in advance. It may be 10 hours, it may be 10 days, it may be even a year a bulb may bulbs life can be varying as much. So, these are the examples where even if we perform the experiment under fixed conditions. For example, the bulb is produced mechanically using machines with a certain material the tungsten and so on. All those things are fixed even the place where we are using the light bulb the wiring the lights which everything can be controlled, but even then how long the bulb will light will keep on giving the light is not known in advance. So, we observe that a large number of natural phenomena phenomena in science in engineering are having the outcome which is unknown and that makes it interesting to study the subject probability because we may feel that if the science is done on a with certain hypothesis and certain conditions then the results are fixed. However, that is not so even something like making of a rolled or making of a bridge on a river. So, that is a strictly an engineering even for example, you construct the bridge using a certain material and make it using certain standardization, but even then the total life of the bridge is it 100 years or is it 120 years or is it 20 years we cannot say in advance because that will be dependent upon the weather conditions the number of floods that the bridge may have to face and the amount of the traffic which may vary too much I mean it may be that the traffic is much less in certain years and then certainly it goes up all of these things will determine the life of the bridge. So, that is how or we can say that the reason for studying the probability theory is that most of the natural phenomena which look like that one could have formed firm scientific rules for that, but they are actually uncertain in nature and therefore, we need to look at the possibilities of various outcomes and then we need a firm foundation for doing so. That means, what are the rules by which we can calculate the probabilities of various outcomes. So, it is not that only theoretical experiments like tossing of a coin, throwing of a die or picking up a card from a pack of cards is the example of random experiments almost every happening in the natural phenomena is actually example of a random experiment. For example, birth of a child what would be the life of a person that means, the age of a person. So, a child is born, but what would be his total age it can be 5 years, it could be 10 years, it could be 60 years, it could be 90 years and so on. So, almost all the activity in human you can say under which we can consider we can we can conceive of they are actually part of the random experiment and therefore, we need to study the subject probability. Another thing which is noticeable here is that when we talk about say phenomena for example, rainfall. So, we may not be able to say exactly whether the rainfall will be 100 centimeters or 120 centimeters etcetera, but over a long period of time if we have observed this for several years, then we may be able to say that what is the probability that the rainfall will be less than 100 centimeters or more than say 120 centimeters or between 100 to 120 centimeters. That means, when we are studying any event in a probabilistic way, we need to look at the long term behavior of the event. It is not one of that suddenly I ask the question that what is the probability that I would collapse while taking this lecture. So, this could be a one of the event because it has not happened and it has not been observed. So, one may not be able to tell the probability of this event, what is the probability that suddenly this roof will collapse where I am taking the lecture. So, one may not be able to answer such questions in a satisfactory way. However, how much time I would take to complete the topic that I am teaching today, I can say with almost certainty that I will take two lectures or maybe I can say that it is around 120 minutes. So, I can fix up a range 110 minutes to 130 minutes. In that case, this is my outcome of taking lectures on probability over several years for students at IIT Kharagpur where I am actually teaching. So, I know that this topic I usually finish in two lectures. So, I can say with almost certainty that in two lectures or you can say with a little variation that two lectures are equal to 120 minutes. So, between 110 to 130 minutes I can complete this topic. So, this long term behavior which is called statistical regularity allows us to study the subject probability because over a long term when we study the behavior of the events, one may be able to say what would be the probability or what is the likelihood of a certain event happening. Now, I will start with the formal terminology of the random experiment on which I can define the probability. So, for that I start with what is known as sample space. So, a sample space is the set of all possible outcomes of a random experiment. Let me look at a few examples here. My lecture on probability it has say 200 students, ok, but every day all the 200 students do not turn up. In a semester I take around 44 or 45 lectures. In each lecture few students are absent. So, I consider the experiment as taking of the lectures and whether the students are how many students are coming. So, if I look at the outcome that how many students the number of students absent during a particular lecture. If this is my random experiment then the sample space can be written as. So, theoretically speaking I can say nobody may be absent, one student may be absent and if I am saying that my class consists of 200 students then on a rare occasion it may happen that all 200 are absent, ok. That event may correspond to some lack of communication like I may feel that it is a working day, but actually it may be declared a holiday which I may not know and therefore, all the students may not turn up for the lecture. So, the number of possibilities here I can list as 0 1 up to 200. Let us consider another example say the time taken to complete a lecture. Now 55 minutes are allocated for taking a lecture. However, when I am coming towards the end of the class I might have started a topic which I need a few more sentences to speak before I end the lecture or I may be able to complete it just before 55 minutes and therefore, after that when there is a new topic I may not need to introduce it at that stage. So, I may take say 50 minutes to 60 minutes just to keep the upper bound because after 60 minutes I cannot continue because by that time the students of another class would have entered. So, I may consider my sample space to be 50 minutes to 60 minutes interval that means, I may write it as an open interval or closed interval 50 to 60. Let us consider the time taken to complete the distance from home to office. Now there may be the total distance may be fixed for example, it may be 5 kilometers, but there may be traffic on the road there may be a railway crossing on the way and therefore, the time taken to complete this distance may vary quite a lot. For example, a 5 minutes distance one may cover in 5 kilometers distance one may cover in 10 minutes, but on other occasions one may take 12 minutes 15 minutes depending upon the traffic or as I mentioned the there may be a railway crossing on the way which may be closed sometimes. So, we may safely put say 10 minutes to 30 minutes time may be taken to complete the distance from home to the office. So, my sample space here in this case can be an interval 10 to 30. The number of passengers travelling in a local bus every day. So, this is a office bus for example, so once again it may have the total capacity say 50 and the number of people who may be travelling in this bus may be from 0 to 50 on each day. We are targeting there is a target practice and the number of shots to fire or to hit a target successfully. So, one may be successful in the first shot he may need second shot he may need third shot and so on. So, I am just putting and so on to indicate the possibility that one may never be successful. There are certain things for example, if we consider finding out a sure shot treatment of a disease such as say cancer then there trials have been going on since time immemorial, but we have not been able to come up with a ready made solution or you can say fixed solution which will work for all the instances of this disease. Although there are cases where that disease is cured, but then there are many other cases where the disease is not cured even if that same treatment is given. So, there is no sure shot you can say solution or treatment which will treat all the instances of this disease. So, if we are looking for a ultimate solution for this problem then may be the number of trials is infinite as far as we are concerned today. I have given examples of various natures here you may look at here the number of entries in the sample space is finite this is infinite it is an interval here this is countably infinite. So, that once again tells that the ways of describing the sample space can be many and the number of entries in the sample space can be finite countably infinite or it could be uncountably infinite. So, we talk about events. So, an event is a subset of the sample space . So, for example, if I say in the first experiment I consider A as 5 6 up to 9 say what does this denote this denotes the event that the number of absentees is between 5 and 9. I may in the say let us consider third experiment the time taken to complete the distance from home to the office I may consider the event as say 20 to 22. So, this means that the time taken to reach office is between 20 to 22 minutes. Say in the experiment of looking at the number of shots required to hit the target suppose I define the event say C by saying 1 2 3 that means, the number of shots required to hit a target is less than or equal to 3 or you can say less than 4 . So, these are various events. So, when we consider the subject probability we are interested in the probabilities of various events. Now, one may just ask the question that whether we should consider all types of events then certainly one answer is that if we consider all subsets of the sample space then that will consist of all the events that means, we can consider the power set of the sample space that would be the ultimate event space. But as I will show you later that it is not necessary that we consider all the events in each instance of a random experiment because one may not be interested to enlist everything. However, let us discuss various kinds of subsets. So, for example, phi is a subset. So, just to say that we can use certain notations for example, I have used a notation omega for a sample space. So, various notations for the sample space sometimes people use capital S, sometimes people use theta and so on. Then various notations are used for the or sometimes the universal set is denoted by U etcetera. So, any subset of that is denoted usually by the capital English letters like A B C D and so on. These are the usual terminology for the events. So, naturally empty set is a subset of every set. The full set itself is a subset of itself. So, these also correspond to certain events. This corresponds to impossible event, this corresponds to sure event that means, this is certain to happen and this will never happen. Now, we when we have interpreted the events in terms of the sets then we can now use the framework of the set theory. For example, when we talk about the sets, we talk about certain algebraic operations on the sets. For example, union, intersection, complementation, taking difference and so on. So, these will also correspond to certain events. Let me explain this. So, for example, union of events. So, if I have two sets A and B then A union B is the collection of the elements which are either in A or in B or in both. Now, when I say A and B are events then what does A union B will denote? It will denote that occurrence of either A or B are both. Now likewise I may consider more than two events. Suppose I have three events A B C then A union B union C makes sense because it would mean that happening of either of A B or C or either of two of them or all the three of them. So, in general we can talk about union A i, i is equal to 1 to n which we write as A union A 2 union A n etcetera. This is occurrence of at least one of A i's, at least one of them occur like one may occur, two may occur and so on all the n may occur. Similarly, we can talk about the intersection of events. In set theory, we know that A intersection B is the set of those points which are common to both. Here it will mean simultaneous occurrence simultaneous occurrence of events A and B. Likewise one can talk about intersection of A i, i is equal to 1 to n. This will mean simultaneous occurrence of A 1, A 2, A n. One may talk about infinite unions and infinite intersections also. For example, one may talk about union A i, i is equal to 1 to infinity. This would mean occurrence of at least one of A i's and in a similar way one may talk about intersection of A i, i is equal to 1 to infinity. So, this would mean simultaneous occurrence of all the events A 1, A 2 and so on. Similarly, we have the complementations for example, complement of A. So, that is A complement. Now, in set theory complement is the collection of those elements which are not in that set, but they are in the universal set. So, here it would mean not occurrence of A. That means, A has not occurred. So, the complement of A takes place. Now, using this one can talk about anything else. For example, if I say A minus B, then this is having A intersection B complement. That means, happening of A and not happening of B and so on. So, one can basically now consider the interpretation of all types of set operations in terms of events. Now, we have special cases. For example, we have disjoint sets. Now, if I say disjoint sets they are corresponding to events, what does it mean? It means that there is no element common. If that happens, then statistically speaking it would mean that if the event A occurs, then the event B cannot occur or if the event B occurs, then the event A cannot occur. So, this is known as mutual exclusion. So, we call such things as so, if A intersection B is equal to phi, we say A and B are mutually exclusive events. That is we can also use the terminology pair wise disjoint. That means, the two terms things taken together are disjoint. We also have another thing. For example, a certain number of sets the union of them may be equal to omega. If that is happening, then we say A 1, A 2, A n etcetera are exhaustive events. Because it means that all the possibilities of the sample space are taken care by A 1, A 2 and A n. For example, if we are considering say the say for example, the weather on a given day and I have descriptions like it may be dependent upon the weather. So, that means, that type of conditions that we may have, we may have hot, we may have normal or we may have cold. So, we can use the notations here A, B, C. So, then this will mean that A, B, C these are exhaustive events. Let us go back to the development of the subject as I mentioned and one of the first you can say formal introductions or formal developments of the subject was published by the French mathematician Laplace in 1898-12 in his book Theories, These Analytic Probabilities. And one of the first formal definitions was given by him which we now term as classical or mathematical definition of probability. So, this is by Laplace. Let a random experiment have say n possible outcomes which are equally likely. Let m of these be favorable to the occurrence of an event E, then the probability of event E is defined to be m by n. So, this is one of the I mean obvious definitions and it is applicable to experiments such as coin tossing, die throwing that is the experiments which actually originated the mathematical treatment of the subject probability. So, in those cases one may assume that this type of conditions will be satisfied like we toss a coin. So, we allocate equal probability half half for head and tail. Similarly, if we have a die and we roll the die then we allocate probability 1 by 6 to each of the possible phases 1, 2, 3, 4, 5, 6 coming up. So, this is based on the assumption that the coin is fair, the die is fair and so on. This is also the drawback of this definition because suppose the coin is not fair then this definition is not applicable. The definition is also not applicable to the cases where we cannot describe the all the outcomes in a proper way. The number of outcomes may be infinite. Just before this I was talking about several random experiments. We considered for example, the number of shorts required to hit a target successfully. Here the number of possibilities are infinite, countably infinite. If you look at the time taken to complete a lecture. So, it is an interval 50 to 60 it is uncountably infinite. In all of these cases this type of definition is not applicable. So, the definition has limitations. So, therefore, it was said that or it was felt that the probabilities definition should be based on empirical evidence. As I was mentioning that we may not be able to say that whether the rainfall this year or next year would be less than 100 centimeters or not, but based on single thing, but if we have observed the whether over past 50 years or 100 years then we may say that out of previous 100 years say 60 time it happened that the weather was the rainfall was more than 600 centimeters and over say 80 we were able to say something over say 70 we were able to say something over 50 years we were able to say something. Therefore, we can fix this number 60 by 100 that is 6 by 10 or 0.6 as the probability that the rainfall will be more than 100 centimeters in the coming year. Now, this is based on the evidence. So, this is called evidence based definition or empirical definition of probability. So, I will just give this thing here now. Trial or we can say also statistical definition of probability. If a random experiment is performed repeatedly under identical conditions and each trial is independent of others. That means, the outcome of a particular trial of the random experiment is not effecting any other incidence of the same experiment. That means, if the experiment is performed several times then what happened in one of the trials does not affect what happens in the other trial. So, this is called independent and under identical conditions means that the experiment is exactly the same. For example, if I consider tossing of a coin tossing of a die or if we are considering taking of the lectures. So, we consider the conditions to be identical. So, if that is so, so the experiment is performed repeatedly under identical conditions and each trial is independent of the others. Now, let us consider some number. Let A n denote the number of trials which result in happening of an event E out of total n trials of the same experiment. That means, the experiment is performed n times out of that A n is the number of trials in which we can say that the event E has occurred. Then we define the probability of event E is defined as limit of A n by n as n becomes n tends to infinity. It means that if this ratio of the number of happenings which are favorable to the event E to the total number of occurrences of the random experiment. If this limit exist then this limit is assigned the probability of the event E. Let me just give an example to show that how you can actually use this in reality. I just mentioned that whether experiment that whether the probability that the rainfall will be more than 100 centimeters. So, what is the probability that the next child which would be born will be a boy or a girl. So, we usually associate probability half. So, that is because the past experience says that usually the child births when they are happening they are equally likely to produce a boy or a girl. Similarly, if we say that the average life of a person is in say USA is 72 years. So, of a male for example. So, it is based on the data of the mortality over a period of time. And it may be the current thing because the average longevity has been increasing earlier it was say 60 years and it became 62 years and so on. So, let us consider a example here. So, I am considering the age of a person at death ok. So, it could be say greater than 60 years or less than or equal to 60 years. If it is greater than 60 years I call it an event M, if it is less than 60 years I call it an event L. And I observe the sequence of deaths at a particular town and it is like the data comes from a hospital or from a sanctuary etcetera. So, suppose the sequence results in MMM this is an artificial sequence here L that means, the first three persons I observed they died at the age more than 60 years then the next person less than 60 and so on. And so, this artificial sequence for example, it results in three being more than 61 less than 60 and following the sequence like this. I want to calculate what is the probability of M. Of course, by looking at this sequence you should say that it is 3 by 4. Let us see that our empirical definition yields the same or not. So, we can look at this what is the ratio of the number of happenings favorable to the event M to the total number of occurrences of the number of trials here. So, here you look at this I can express as something like 3 k by 4 k if n is of the form 4 k. It is 3 k by 4 k minus 1 if n is of the form 4 k minus 1 it is equal to 3 k minus 1 by 4 k minus 2 if n is of the form 4 k minus 2 it is of the form 3 k minus 2 by 4 k minus 3 if n is of the form 4 k minus 3 for k is equal to 1 2 3 and so on. So, if you look at this then limit of this sequence here if you look at this this is 3 by 4 this is 3 by 4 this is 3 by 4 this is 3 by 4 as k tends to infinity. So, we can say that the probability of a person achieving age more than 60 is 3 by 4. So, here you can see that it is empirical definition being applied here. So, likewise for most of the real life phenomena which I was discussing in the beginning of this lecture in all those situations one can apply empirical definition of probability to obtain probabilities of various events. So, one may say that this definition is almost you can say universally applicable, but even then it has certain limitations. For example, one should be able to observe the experiment although you may not be able to conduct the experiment, but you should be able to observe the experiment and what is the outcome of that and sometimes that may yield falsified thing. For example, you may observe the outcomes, but you may not be able to look at the outcomes in its entirety and therefore, some data for example, you have put some machine to record and that machine is malfunctioning or some person a human being is collecting the data and he may get a wrong figure. So, these are the drawbacks of this empirical event. Secondly, one may not be able to conduct the experiment as I was mentioning that the experiments are rare which may not happen so often then also the application of this definition is not possible. For example, I was mentioning one of events so in those cases if somebody has not observed that kind of events then one cannot find the probability of that. Another thing which could be misleading is for example, one may feel that if it is an impossible event the probability is 0 the converse should also be true like if the probability is 0 the event should be impossible and similarly if the event is sure you have probability 1, but if the probability is 1 the event should be sure even, but one may have this kind of occurrences. For example, I may have a n is equal to n to the power 2 by 3 and so if I look at the ratio a n by n then it is n to the power 2 by 3 added by n that is equal to 1 by n to the power 1 by 3. Now, this goes to 0 as n tends to infinity. So, this would mean that the probability for this event for which the number of favorable outcomes is n to the power 2 by 3 is actually 0, but this is not an impossible event actually the event occurs, but the ratio of the occurrences this converges to 0. So, one may give interpretation in such a way that the number of occurrences is actually progressively decreasing like if I say n is equal to 1 then a n is also 1, but if I take n is equal to 2, n is equal to 3, n is equal to 8 for example, then a n is equal to 4. If I take n is equal to 27 then this will become 9 that means the ratio is becoming much less and progressively it is declining to 0. So, it is not an impossible event, but in the long run the probability of occurrence of the event would be negligible. So, that is the meaning of this and one may have the reverse of this also that the probability may be 1, but the event may not be a sure event. Now, to overcome this drawbacks of both the definitions although we may consider them as now the methods of calculation of the probability. The Russian mathematician A. N. Kalmogorov laid the foundations by giving his axiomatic definition. So, for this one now we have a sample space. So, omega is the sample space and as I mentioned that by events we mean that any subset and one may consider all subsets also, but in a complex random experiment it may be quite complicated or it could be quite difficult to enumerate all the events and then look at the possibilities of that and it may not be of much interest also. For example, when we are discussing the rainfall, the amount of rainfall then certainly it could be like it could be a drought that means complete drought is there, it could be 10 centimeters, it could be 15 centimeters, it could be 200 centimeters, there can be a super cyclone in that period and so on. There can be thunder storms, lot of possibilities are there and if one wants to study it could be a very complex description of the sample space. But an average person or an average weatherman or an average farmer may not be interested in all of that thing. He may be interested only in the information whether there will be an adequate rainfall or not. So, if we say that then I am looking at only two events. I may say A is the event that the rainfall is adequate, A complement is the event that the rainfall is not adequate and I am not bothered about anything else. Therefore, we should have a framework in which we can limit the number of events that we may be considering. So, we consider a structure. So, B I use a notation script B, it is a class of subsets of omega satisfying the following two assumptions. One is that A belongs to script B implies A complement belongs to B. That means for every event its complement should be there. Secondly, if A 1, A 2 and so on belongs to B then its union must also be in B. That means for any collection of the events its union will also be there. As a consequence one may check that if I say A 1, A 2, A n and so on belongs to B then this would mean that intersection belongs to B. We may consider monotonic sequences, monotonic sequences, then if A n is monotonic then limit of A n also belongs to B and so on. So, all types of possibilities are there. So, simplest example is I just now mentioned I may consider phi A, A complement and omega then this satisfies this.  All possibilities will be there. This type of a structure this is called a, this structure is called a sigma field or sigma algebra. So, what I am saying is that we need not consider the class of all subsets of a sample space, but we may restrict attention to few events which are of use to us and they should formulate or they should form a structure that is structure we are calling a sigma field or a sigma algebra. Then we define probability function p is from omega into r satisfies the following three axioms. Let me call it p 1 that is probability of e is greater than or equal to 0 for all e, p 2 probability of omega is 1, p 3 is that if e 1, e 2 and so on are pair wise disjoint events in B then probability of union e i is equal to 1 to infinity is equal to sigma probability of e i, i is equal to 1 to infinity. So, these are called axioms of probability and now I am just defining p to be a function which just satisfies this ok. Now we will show that this structure is enough to consider the probabilities of various kind of events. We will see the consequences of this in formulation of certain rules of calculation of probabilities of various events. For example, probabilities of unions, probabilities of intersections we will use it to define conditional probabilities and various other things. So, in my next lecture I will elaborate on this axiomatic definition how to use it and we will discuss certain examples before moving to the concept of random variables and probability distributions.


I think it's a great place to start when I was a kid growing up in DC thanks to your dad amongst many other people but but certainly helpful from him you know advocating to help so be a jury how did you know about that because I grew up in DC and I'm Jewish probably like held the same signs yes in front of the Soviet Embassy yes yes free Soviet Jews and this was because your your father but I have to do much either the hardest I had to endure was having Soviet Jews sleep on the floor when I'd wake up I'd be my mom would be like here's someone I just had to negotiate around like the neighborhood women terrifying for my adolescence but I couldn't get over there your father was held hostage you know in all the times I've ever done interviews this has never come up before your read your the failings of researchers that you have that's just amazing yeah my dad my dad was held hostage by the Hanafi Muslims in I was in high school in 77 along with about a hundred other people it wasn't just him yeah they took over the neighborhood building where my dad worked the Islamic Center and the DC the district and then we got a picture of him from your website because there's a great story on it that you wrote about his food issues yeah food issues we all what Jews don't my dad my dad he had no palate except for salt so he was the quintessential Jewish eater he could taste salt he could taste two flavors one of them was salt and one of them wasn't and that was him and yeah it was it was a frightening thing and I grew up in that household trying to get to other food groups but the other thing about my dad which about the Hanafi thing was this is a true story I have to tell this now because you brought this up I got to go with it I was in high school I was a junior in high school and that you know how you'd like you know you're I was trying to be the class clan I was acting out there was a girl named Margaret Bernal who had big eyes big traffic light eyes that's the only thing that were big that you noticed what no yeah I was I was pure but I just had a crush on her and it was it was six period English and so we had this substitute teacher and I was like I tortured the substitute you know how that goes you know I could class clown ruining the class for the substitute and I went so far that I knew I would be in trouble the next day I knew this so fifth period I'm in the student newspaper office and the phone rings it's my older sister and she says you gotta I come coming to get you there's something going on at the building dad's been taken hostage turn on the TV I'll be there in 10 minutes and I turn on the TV and sure enough it's on all the DC's channels that they've taken over these buildings and I went to my sixth period class and the head of the English department and the teacher were both there waiting to punish me and I mean I think I was probably suspended I mean it was just they were so furious and I walked into that class and I swear to God they're there at students who will still remember this who went to high school with me I said BCC yeah BCC I said I said Mrs. Galger I'm really sorry my dad's been taking hostage by a group of crazed religious gunmen I have to go so and she she and Mrs. Her they followed me down the hall screaming I mean the kids in the class were like man he's really gone over the anyway I came back on the Monday after obviously on the month everyone knew what happened a few hours later but I came back on the Monday nothing was ever said ever it was yeah were you grateful to him just for getting out hostage I was almost grateful to the terrorists I mean you know it was just I'll never I mean I said it even as I said it I was like you really shouldn't be joking about this but I couldn't help it it was just there and your mom went back to school and while you were in college at the same time and she I understand graduated 5 8 Kappa while you were failing out it took me five years to she beat me out of college she's she went back to school she dropped out a hundred university a hundred college here when she was in her 20s to get married and she went back and she was like taking 9 12 credits a semester and she beat me out of college I took me five years five years in two summer sessions it's kind of humiliating well it's humiliating but it's also humiliating but the education system because at the same time you're getting more bylines than hired writers I believe at the Baltimore Sun you were interning at the Baltimore Sun I find all this research into the esoteric of my life to be unnerving and inappropriate can't we just do the usual like why'd you kill stringer bell shit


This was an unprecedented opportunity to bring together industry policy and consumer interests and in particular to look at an evidence-based way at what would drive financial inclusion through digital financial services. And what I particularly liked was that it was a chance to meet with telco regulators and telco industry representatives as well as the more typical central banks and financial institutions that we usually work with and bring in consumer perspectives very clearly. Yes, well I think we saw very clearly out of the whole body of recommendations a few key points that there's need for innovation and that regulation and policy can permit experimentation but it needs to be closely watched as well to be sure that there are guardrails around consumer protection issues for example to deal with security and the whole ecosystem and to make sure that the fundamentals are being built towards sound future growth. I think a few other interesting points are that the clearly the long-term goal for this work is economic inclusion so it's financial inclusion in the service of economic inclusion and more and more conversation about the second generation issues, competition and credit and so on that will speak more directly to the growth agenda.


Hi everyone, Joe for jaspyscasebrakes.com, happy Saturday coming at you with a quick two box break of 2019-2020 Panini Contender's Optic Basketball. This has been a popular one when I'm breaking 98. Break credit helps too. Big thanks to all of these lovely people for getting in on the action on this two boxer right here. Thanks everybody. Matthew with that triple last-bond mojo, getting that middle group of teams there. Thanks to him. Thanks everybody for getting in on it. If you bought at least two teams, you'll have a chance at getting some break credit. Right here, we marked those box with X's so you know they're from the same case, and we just load up another two box break. We can do two more of these. One autograph per box on average, redemption on the bottom. Any guesses on that redemption for bragging rights? All right, there's Andre Drummond at Uniformity for Eric and the Cavaliers. We got Donovan Mitchell, Cracked Ice, Playing the Numbers Game Insert for Gary and the Jazz. We got Goran Dragic, Silver for the Heat, Matthew Shearer, a Fox in the Box, Deer and Fox for Oliver and his Kings. It's to 99, and oh, I guess I didn't have to really hide that because I was a redemption. There's John Collins for Atlanta, Nicholas. All right, and let's see what this is all about. Good luck. No one's guessing. It's going to be Admiral Schofield, Rookie Variation Season Ticket Autograph, Admiral Schofield for Nicholas and the Washington Wizards and a free top loader as well. All right. Next box. All right. There's Historic Slamms, Zach Levine, Dunk Contest winner, and there's Front Row Seat, LeBron James. We'll see him in action tomorrow against the Suns. That should be a really good series. Lakers, Joseph Matthew Shearer gets the Blue Ice, LeBron James, Front Row Seat Insert. I'd like to get some Front Row Seats for a Lakers game. There's Tim Hardaway Jr. I feel like he had a pretty good game today against the Clippers. Let's go to Dallas, maybe for Mark. And there's Tobias Harris. I think Sixers are in action maybe tomorrow. And there's Eric Kay with the Sixers. And behind Ceejin McCollum is the Autograph. Ooh, I think it's a nice one. It is a nice one. It's RJ Barrett, Rookie Ticket Autograph. The Knicks are in the playoffs. If he has a good series, RJ Barrett, we can see the cards to the moon. Adam Kelly with the Knicks. There you go, Adam. And that's 18. 16 out of 149. Kind of hard to see in the lighting at this time of day, but there it is. And there you have it. Nice two-box break in the books now. Let's give away some money, money, money. All right, so let's flip back to this list right here. There are the instructions. I'm sure everybody read this. Top five, $60 a break credit. So let's sort by your first name here alphabetically. Adam got two teams. That's an entry. Brandon got two. That's an entry. Eric Kay got four. That's two entries, basically by an even number of teams. Gary with two. That's an entry. George with three. For the purpose of the promo, two count, still an entry. Matthew Shearer, same thing. Three, two count, one entry. Michael Schwartz, two teams, an entry. Nicholas, six teams, three entries. Oliver with two teams, that's an entry. Shane with two teams, that's an entry. You've got Shane, Oliver, Nicholas, Michael, Michael Schwartz. Michael Floyd only got one. Matthew, Mark only got one. George, Gary, Eric, Brandon, and Adam. All right. I want to make sure I got everybody. All right. So once again, top five, we'll get $60 a break credit each. Here's some new dice. There's the new list. Let's roll it. Let's randomize it. Four and a three. Seven times. Lucky, seven times. One, two, three, four, five, six, and good luck, seventh and final time. After seven times, there you go. Top five with the break credit. Congrats. Congrats. Congrats. So Shane, $60, Nicholas, $60. We'll send those in the same break credit code. So $120 going your way. Brandon with $60 and Michael Schwartz. There you go. Thanks everyone else for giving this a shot. I appreciate it. For those of you here, check your emails. Check your spam folders. It'll arrive to you as a gift card code. Thanks very much. I'm Joe for Jaspy's casewrakes.com. I'll see you next time for the next one. Bye-bye.


What's going on in front of them? Welcome back to another video. It's your girl Janisse. If you guys are new to the channel, make sure you hit that subscribe button and join the family. Guys, today I am going to be telling Isaiah why I love him nonstop. Now this is not gonna be a prank. Isaiah knows that we're vlogging, but I'm just gonna be really extra and I'm just gonna be continuously telling him why I love him, the reasons why I love him, give so many explanations. I'm just going to try to be super, super extra. Isaiah right now, it's outside. He's talking to one of his buddies. So when he comes in, we're gonna start the vlog and we're just gonna take you with us on our beautiful day. So if you're ready for today's video, don't forget to smash that like button and comment team Janisse in the comment section below. Let's get it. What's going on in front of them? Welcome back to another video. If you guys are new to the channel, make sure you guys hit that subscribe button and turn on your post notification bell. Leave a positive comment down below for a chance to get a what bit. For a chance to get a shout out in the next video. That is right guys. So today we have to go to salon. Janisse is gonna be dyeing her hair.  The same color, I'm just retouching my roots.  To the end of the video, I'm doing a crazy color and it's just gonna be black. I don't wanna disappoint them. Nah, yeah, that would be funny though. The comment section would have been crazy. We're also gonna go grab something to eat here at a restaurant that's close to us and then afterwards we're gonna go pick up a new camera that we ordered at my mom's house. I'm honestly really, really excited to go see what that camera is like. It's really small, smaller than what we have now. I feel like what we have now is like a dinosaur. But I'm really, really eager to try out the new camera. It's supposed to be like the same quality but it's supposed to be smaller. Oh, I love how cute you are. Like you always just get excited for like technology stuff. Okay, thank you. Okay, well with all that being said, guys, we're gonna go eat first so we'll see you guys in the car. Made it to Maggie's, all right? So what are you gonna get? So I don't know cause I have to look at the menu cause I gotta eat healthy, you know? She on the diet, she on the dieta. All right, so what am I gonna order? I already know. You're not gonna be able to guess it. What? I'm getting a salad. Boy by you is not getting no salad.  He is getting calamari. Okay. Right? Okay. And buffalo chicken sandwich. Okay, Peter, give me that. You think you know me or something? I do know you. That's what I'm talking about. You think we'll get to meet Maggie? I wanna meet Maggie, I'll never get to meet Maggie. Babe, you're so, I can't but honestly, I just love your sense of humor. So you admit I'm funny. Sometimes. Let me hear it, say it, you're funny. No. Let me hear it. You know, you just have a good vibe all the time. That's all. She knows I'm funny. She just don't wanna say it. But it's okay. We'll see you guys inside. Babe, are you full? I'm full. Yeah. I feel like 15 pounds heavier. Ooh. So yeah, that means you're full. I didn't finish my food yet. I'm sad part. I love how you're always like holding food for me. You're so sweet. Like you hold like bags for me, food. Of course.  I gotta make some strength. No, I gotta get stronger. Okay, okay. So guys, like I said, I didn't even finish my food. That sandwich that I showed you guys, I ate half of it, didn't even touch my fries. That's sad. That's just sad. I do this every time. He asked me too if I wanted fries and I was like, yeah, yeah, give me fries. And I had, I was like, why did he do that? Cause he's definitely not gonna do that. Every time. It only happens when I order the calamari. When I order the calamari, I never finish my food. So guys, calamari slaps. Like, I don't know if you guys have had calamari. I obviously didn't have it cause it's fried. But Isaiah's taste in food is amazing. Like I love how you have such a great taste in food. Like you get that stuff, of course. Okay, I'm not gonna argue with that. Anyway, I wouldn't say it's the best choice of food because I eat a lot of unhealthy stuff guys. And I'm trying to, I say this like, I feel every other vlog I'm trying to turn over in the leaf, the leaf has not been turned. I'm gonna try to start Monday though. I'm gonna try to start living a better lifestyle. I'm gonna go to the gym consistently starting Monday. As far as the food part, I'm gonna slowly try to start eating healthier. No promises though. But that's gonna be like the biggest part, right? Nutrition is the biggest part. Yeah, I would say like, I've been like on a nutrition journey for a little while. And like, I noticed like big results. I'm not gonna talk too much about it cause I have plans for it in the future. Ooh, spoiler. But yeah. Oh my God. Would that be a sight guys? On to, where we want to the salon please? Now to get your stuff? Yes, cause I need to dye this hair and my roots growing and it makes me look like I'm balding.  So we're pulling up to the hair spot. Babe, I just wanna tell you that I appreciate so much the fact that every time that I wanna do something like, I love that Isaiah just goes and like, he supports me. For example, my hair, he will literally help me dye my hair. He will take me to get my hair dyed as soon as I need it. Like, I just love that about him. Like, I love that he always is so supportive in everything that I do. It comes with a form of payment, man.  Back, for the rest of your life.  Oh, I don't know about every night. I'd be tired sometimes. Guys, that sounds like fair to me. I don't, that sounds fair to me. I don't know about that. But anyway, we'll see you when I get my hair dyed. I almost just stole a comb by accident. We were at the register, she was ready to pay for her stuff and I'm just holding this comb in my hand on my phone, not even like paying attention to anything.  And I was like, oh, I almost walked out the store with it. Listen, I think that it's so funny cause the girl was like, oh, he's like a little kid. You know how those moments of a little kid is just like, you have to remind them to give you the stuff for the register. I think it's so funny because I love that Isaiah gets so into the stuff he's passionate about. The reason why he was distracted is because he was looking at car parts. This is true. Yeah, exactly. So I love that he's so into the things that he loves. Oh, you're loving me extra today, man. You're loving me extra. I don't know.  Not this much. Today you're doing a lot of it. No, I'm not. Yeah, you are. You're delusional, but anyway. So now I think it's time to go ahead and get the new camera. I'm so excited because this camera would be making my arm hurt, honestly. The camera's biggest how it would be heavy. Let's go get this new camera, yo. Let's go! Pocket size. So we just got in the car. We were getting our packages and Isaiah's grandfather made us some soup. Oh, he's making something, man. The man all of a sudden loves to cook. It's so freaking good, guys. This soup I'm literally obsessed with. We're gonna split that because I like that soup, too. I didn't say it was off for me. Oh, okay. I'm just making sure we're gonna split that. But guys, got the new camera, yo. Look how small this thing is. It fits in my hand. The one that we're using right now is like a dinosaur. It does not fit in my hand at all. It's true. It's super heavy, too. Yeah, and this is like, I don't know. It feels like a feather to me as far as the camera goes. But, guys, let us know in the next video because the next video will be recorded off of this camera. So, let us know in the next video in the comments. Do you guys prefer this camera or the one that we're recording off of right now? We heard a lot of good things about this camera, so we're gonna give it a shot. So, guys, with all that being said now, we're gonna head back home, finally. I am low-key tired, and we didn't even do that much there. We didn't do a lot. I think it's just because we were so excited that the weather's nice. I think that's what it is. That, and I woke up really early and I couldn't go back to sleep. But, whatever, we'll see you guys back at home. So, we are back home. Look at that. Come here, Nanny. Come here, daddy, look. Look at you guys. What's up? Is he a friend? Is he a friend? Oh, my baby. Come here, Nanny. Babe, I love how it doesn't matter how tired you are. You always play with him. Why do you keep saying things you love about me? What do you mean? You've been doing that all day. I know. Why? What are you doing? Nothing. I just told you how much I love you. I can't tell you how much I love you and I love the things that you do. Yeah, but you've been saying it. I'm sorry, Nanny. Here, go play. Did he just squeal because he won his toy? I don't know what he did. That was a weird noise. But yeah, you've been doing it all day and that's more than like usual. Every now and then you're throwing like a little thing. Yeah, but today has been like nonstop. Well, since we're already home and you caught on, it's kind of frank, but not really. It's not a prank. You know what I'm saying? It's not a prank, but... You ain't getting no W on your belt. There's ain't no prank. Yes, I did because you were questioning me why I keep saying how much I love you. So I basically said... It's not a prank though. It's not a prank, but it kind of is. So what W did you get here? I got a W and you got a W because you know now how much you appreciate it and how much I love the things that you do. And I wasn't lying either. I did love all the stuff that I said. Well, I got my real W six years ago. Ooh, that's on period. And today's video, I hope you all enjoyed. If you guys did, again, don't forget to smash that like button. Comment team Janice in the comments section below just for the hell of it. And then it's time for today's post notification shout out. Today's post notification shout out goes out to Francisco Maldonado. Thank you so much for your love and support. Isaiah and I love you. If you want a post notification shout out, all you guys got to do is like, comment, share, and subscribe. And turn your post notification bells on to you notified whenever we post a new video. And with all that being said, Danette and I and Dada will catch you in the next video. Love you.


This is like the introduction set of a project that kind of has two different hats or maybe even three different hats that sometimes you'll hear in the presentation or what we're doing that we may put on my on once in a while. And one of them would be as an economic development director. When I returned home from college, I'm actually a consulting meteorologist. I returned back to the community to start that business working with local ag producers. And I had parents that were ill at the time and six siblings in the family to help the family transition the family farm. It is a 1200 it's two sections and then we have another half section located not next to the original two homesteads. But it is not what we're seeing in today's farm size and scale, which you would you know needed to be a successful commodity operation. So in this fifth generation transfer to my generation, I was part of my family's will that this operation could become viable for at least multiple of the six of us. Five of us live in the community all working professional jobs outside of the family farm and looking for a way to move in that direction. Obviously, with my background in meteorology and climatology, sustainable farming was something that is in my career realm. Part of the reason I moved back from Kansas City to the home community was to be one open spaces, be closer to the farm, watch my nieces and nephews grow up, but also to apply my college degree. Microclimate is very much part of what is in part of sustainable farming. Permaculture, zero escaping, things like that can all be applied to these sustainable techniques. But out northwest Kansas and commodity ag world, this is, you know, we're talking 10, 15 years ago when we made this decision and started this work, it was the odd duck, the odd ball, the crazy idea at the time.  So you got the economic development director hat there, the local farm hat, and then my role as the vice president of consumers for the co-op is a co-op of originally northwest Kansas farmers that now has expanded to 50 farms in three states. That's that tri-state area in the corner. Like we said, this was a out of the box idea 10, 15 years ago. So these farms had to go to the Denver market for our market. It was not local. We didn't have lots of farmers markets or the economy out there is not conducive for direct selling cells of meat. So that little background about the co-op to start this off kind of set the stage for the farms as they grow into the co-op and become part of the process. It's a producer. So actually this came into the economic development office when I served as economic development director the first three or four years I moved home as a part-time job to supplement the weather. It was Rocky Mountain Farmers Union, Oglala Commons organization that was working on some youth return home initiatives with the hometown competitiveness model in northwest Kansas. This concept formed based off of the Oklahoma food co-op which was getting some notoriety and success in the late 90s and early 2000s. So it is a like Oklahoma producer and consumer member co-op. You pay $100 to join the co-op and you can do volunteerism or be part of the co-op as a buying member. In particularly we started in the Denver area with about 30 customers and then producers are also a member and same thing $100 to become a producer member. It is bylawed in to be board controlled by the producers. So that is how it maintains a producer controlled co-op. So by the board structure it is driven by the consumer or by the producer. So my role as vice president of consumers is to develop new markets and strategic planning as the co-op grows. One is the online farmers market modeled after Oklahoma. Direct sales to customers. It is an online ordering system. They order from whichever farm they want, whichever item and then we distribute it, drop it off and trucks and trailers return back to the home originating site which is in northwest Kansas. We are now transitioning to a regional food hub and aggregator. So we are the first mile aggregator to the producer. Our drop off points and delivery sites in Denver are the last mile to the consumer. We are picking up some first mile back that comes back to northwest Kansas. We can talk about that a little bit later that is developing some backhaul and part of the northwest Kansas food work that is doing programs more to start on the food justice side markets but eventually maybe helping grocery stores and other farmers market with some of their supply issues in the communities as they get up and going. We got one that right now, we got 1,000 products. We go two times per month to the direct sales during the season. During the winter months it is one time a month. Actually on that direct sales side November is the number one month. We just did over 100 orders yesterday because of Thanksgiving and our turkeys. Our mission and values are we are producer and consumers uniting in the interests of locally grown food. We want to be environmentally sustainable economically viable and socially just and cultivate the farmer-consumer relationships. This last thing is the number one core value in the original board of directors which were all pretty much northwest Kansas producers are in that tri-state area. We did have some consumer members from Denver but they were in part of organizations that had that same mission. It is to revitalize our rural communities. If our rural communities and this sustainable farming is not part of that development piece it is critical to the survival of the community. That is naturally ingrained in our environment where our production and producers are and still the number one or driving mission of the co-op. This map kind of shows you the infrastructure of the co-op, our customer base obviously is a Denver. Our sorting location hub is right here in the middle and then our aggregation hub where the product kind of comes up. We have a truck that comes here and we got a truck that comes up from the Nebraska producers up here, comes down and we meet and aggregate here. The orders get sorted and then dropped off in 21 pickup hubs back to these clusters of people. On this map it is showing the aggregation, distribution and processing infrastructure. Every one of these blue sites are one of those pickup hubs. The yellow sites are our collection aggregation centers where say 12 farms in this area come in, collect here and then it collects and collects and goes down the interstate and same way here it collects and collects and then eventually gets there. That is what we call aggregation. These blue are actually distribution so when the trailer is here we leave at 7 in the morning, get here about noon, distribute, it goes out, trailers get back here, 7 p.m. on Thursdays and then these blue route is run on a Friday and then our weekly route runs out of Bennett on Fridays to the restaurants and stores downtown in Denver. These things are critical here. These are your USDA processing facilities. So that is what makes the clusters where the farms are. Kansas initially had more processing so it made more sense why we had farms already doing this a little bit and the capacity to start out here and this was such a void. Kansas has the state and USDA inspection since we are moving across state lines we have to have the USDA so these are all USDA. There is a combination of mobile processing and fixed facilities in here and then you get to Colorado and you kind of see what is happening here. They have lost a lot, it is bigger, people have tried, they do not have a state inspection system so it has created a lot of void around that processing. So basically like I said we have a core group here, we are developing, this is an up and coming group, there is a lot of specialty crop production going on there and then this Colorado, it is basically from Bennett, Colorado to Colorado Springs, another group of farmers that are smaller type farms but again there are still main markets coming in there. We do have a co-op down here, a partner co-op on the Ark Valley, one in the Salida area of Colorado and one in the Southwest that comes in here, collects into the system, eventually connects in Bennett and can backhaul and move up and down this area. We have a market set in here of 6 million people. The food hub definition here, this is what the USDA defines as a food hub that is where the co-op is moving more in direction. We are very unique because when you think of a food hub you usually think of the urban definition which you have Philadelphia, East Coast, Sacramento, Portland. Out here in this high plains region, our population center is Denver but high price of land and this distribution and lack of processing, it is a whole different landscape out there when we talk of hubs. The USDA definition is manages, aggregation, distribution and marketing of source identified local and regional product and these are the markets that typically a food hub works in. Again, we had to start retail because we are very, very small farms. They had to become sustainable, learn, grow, learn the rules and regulations. As we go, we are just starting to enter into some of this volume, retail thing and then eventually the big demand is going to come from these food hubs is how do we service the institutional markets, the interest and the market is there. This distribution and processing and system is in place. Local food system has lots of gaps in this part of the country. The key thing to take from this here is five to ten anchor producers, USDA statistics say that it takes 600K to one million to sustainably run the food hub function of what we are doing with the food co-op and history shows that it takes seven to eleven years to get there. Times are changing, the window of opportunity, the market demand, things are pressurizing there, they think that's now three to seven and that in our particular case since the distance we are working with in the area, we are probably more closer to the million plus before it works for the food co-op. The aggregation part, you hear that term, what is it, just to give you a little bit of an idea, it's the meat of the co-op or what we do. My position was to connection relationships and creating the market opportunity, then we source the product from the farms, links that production with the needs that we've identified in the market and do the logistics to get it there, that's the drop sites, the label, the tracking, the pickup delivery, the sorting, the distribution and the more important thing is we keep that value chain from the producer to the end consumer. It is the know your farmer, it's the I want to know where it comes from, I want to know if my producer is organic and the website allows that to be listed individually by the farm, the farm controls their prices, we have a percentage that is on the consumer side of 10 percent and the producer side of 15 and we try to average around that 20 percent margin similar to other food industry type businesses, so it is a low margin, intense infrastructure type business but we keep that value chain to stay in the local food or sustainable business model. This is the history of the co-op, the sales, the only thing I want to hear, this was the direct sales side of the co-op is producers learn and grow, we saw a little bit of a jump here that year, we basically some of this change in here to here was due to some website and internal changes and then here you're noticing that volume side taking effect, it's changing the dynamics of the co-op, we're nearing this, we are in twin age stage now where we're still volunteer board, we got a few part-time positions but now we got to start making serious changes as far as you know what we're going to do is a co-op to be sustainable. This obviously being a producer in the co-op and the presentation topic here is poultry, we had some meat, our limiting factor on the meat is the processing, so we have been had to form an entity to raise chickens, process them and then enter them into this market demand. You've heard the other forums in this conference talk about poultry, that's the money, the interest opportunity, you heard the processing issue coming up to solve that but when we did our expansion plan studies it said the capacity, the ability for all these forums to do some poultry production, enter into this system and go to Denver is probably the leader or the first entity or first product to become an anchor product in the system, follow that with specialty crops because that's sexy and that's the highest demand thing, if you can grow the specialty crop producers work on that at the same time and then work on this processing and start building up meats and grains and some of the other items that can go into the system to build the food hub. So here's our history with High Plains poultry or our first poultry farmers were several of them, I think there might have been of the 12 at least five to half of them had poultry on the farm selling at the local farmers markets eggs or trying to go into schools and that so so we we had these small orders going to Denver in 2008 and 10 that kept that system kept on going and then in 2011 we're like hey here's some opportunities so the poultry farmers started growing and at that time we had to go to McPherson, Kansas so you can imagine what was going on we'd had Colorado farmers picking up chickens all the way back to McPherson you drop them off have to go back home and then send another vehicle to go pick them up and come back and very cost inefficient and then one of the producers in in Atwood at Rawlins County area decided well we're going to go ahead and invest we want to grow as a beef producer expanding the poultry side of the meat business because we're going to do poultry bought the processing equipment to basically do it on the farm but we had to do it USDA so they because of a ostrich license at the local processing plant allowed them to have the ability to do poultry in the facility so basically the farmer rented the kill room and the date on one day a month or whenever when they weren't killing they use that room to process the poultry in scale and start moving more poultry through the system. 2012 we did that expansion plan that said you got the infrastructure there go for it with the eggs and the meat that's where you guys need us or where the co-option start foking its attention and then the group of farmers in 214 said we got to figure out a way to do our processing because we're in the local guys way and we're tired of going to the person so we did the serigrant the rest of this presentation will go into the process of what we did during the grant 2015 we ended up deciding to construct an MPU which is part of the serigrant process and then as you saw in the growth of the co-op most of that growth or about 28% of it is the meat and the eggs the rest is we're now we're able to go weekly we do have some beef going into that system and some of the specialty crops so there is a small percentage of that growth that is opening the ways for those other farms now to to grow their markets as well so our seri project this was our performance targets and objectives we wanted to organize first estimate the startup and operating costs of a at that time we were looking we were still thinking fixed will this thing be mobile we still built it as a mobile but it's really fixed at this point determine the feasibility find a site do the permitting that's required both locally state and usda federal equipment purchasing and fabrication implementation startup and develop a plan to enter that co-op market opportunity this is the outcomes and the impacts as you can see we got the plant up and running in october of 2015 and the co-op that was the first year we were able to really deliver through the winter with a with a with a product item so we did 600 chickens and 23 turkeys at Thanksgiving this year this year we are I you know I think this is this was a close estimate to where we're at at the end of the year and we just did our turkeys um so again it's an estimated total and this in our projection feasibility is where we thought the processing plant would end up in 2019 fully use utilizing the crews and what can be done in the unit that we built our revenues this was from these right here this is what you saw in that graph for 2016 that 25 percent of that 400,000 and this is what this would do in 2019 and then as far as the farms go right here it was two farms right here three or four and then here we could be up to 12 working in this facility our other outcomes and impacts we wanted to increase jobs obviously because the economic development 2016 it was family part-time labor this year we have paid four to eight part-time workers operating two three two days processing one day packaging and then we have this projection for 2019 again I brought this back up to uh really highlight that 100,000 increase in the co-op sales is sitting here for an anchor producer if we can get four or three more of those say a hydroponic vegetable facility something else creating that same volume we're on our way to to be an sustainable and viable food hub okay back to the MPU here we we started up our accomplishments we formed an entity for four farms to be able to invest into the we didn't take other than the funding that we had in the SARA grant we actually formed an LLC to invest with four farms we did the startup business plan fabrication and budget did the financing within our original SARA grant I think we had 15,000 of it going to the infrastructure and equipment and fabrication costs and and then the rest was equity investment from each of the farms the feasibility obviously our current situations weren't feasible uh this is was where we're still kind of at and this has to do uh we we decided to go mobile by looking at we toured uh went to ballman's uh Anita's and watch what their fixed facility did we went to Cali crates uh in st francis beef processing plant then we went to Taos New Mexico and saw where they had a mobile unit that was fixed and doing all sides kinds of livestock in it lamb pigs one day they had some pulled you know they they were doing everything in Taos um a site location travel available labor took all that into consideration uh when we did our economics on it we're from the McPherson stuff we were saving three dollars per bird thought with those numbers of I always showed up there we figured this unit will break even operational costs sometime next year around the 12,000 to 15,000 chicken per year mark and we started I think we're at 450 for processing of a bird if you're cutting it it's another cutting them up into parts another dollar 25 give you kind of an idea what the costs are this is probably the biggest variable we thought we were going to do this in three or four months and be up and running last June we didn't start till October last year so it took us 14 months to do that and this was probably the biggest reason for that we did have some since we farmers built it ourselves particularly the lead of one of the farmers who was looking at doing this anyway on their own um um so we with there was some time to fit into our personal farming schedules that created some time but the biggest was the hoops to get USDA state all these food safety regulatory issues in line and understanding them and knowing what we were doing I don't want anybody to get the the notion that the USDA is against or all the things you hear that why you can't do this they want to work with you it's just new to them and they aren't staffed and you're you're dealing with regions and moving employees for like our ffs is had to come from Arkansas our everyday inspector that has to be on site had to be trained because he's never seen poultry in his life being in Kansas so we had you know it's all that took time to put it together and then everybody's receptive that USDA we want to learn how to do this because this is an opportunity for for everyone uh that is food safety inspection something this is hazard critical access point plant you know the within the plant every food safe point critical point where a bacteria could develop on the chicken you have to have a check and the process in place uh standard safe operating procedures so that's your plan to all the way through from the cage into the plucker and and all your processes are keep the mice out of the facility clean bathrooms you name it it's in there um and uh you know there we had to take our one of our farmers you know took the training and did a lot of this work you know internally so we owe a lot to to that process there uh our scale up plan um this is basically what what we're what them numbers showed you uh 500 um as we speak we can capacity to go to that uh 100 a shift does uh because of this a shift of five to seven it's like we got seven people on a shift can do if they're really good they're getting up here around this number in three hours that's about how many birds we process and since we air chill them these are going into the air chiller and you have to have them down to 40 degrees in three hours and then afternoon the inspector has his eight hour day and so that's about all you can do in a shift now you could run two shifts have two inspectors you could go to more days a week and bring in another inspector but that's down the road uh we uh that'll take time might it be a new might have to be a second inspector um so those are some things that that either slow the growth or put you in this plan and again that break even in 2017 okay here here's our design we ended up we we purchased a reefer trailer and then um if you saw the picture here we actually this processing there's a our local vet office is here and this is just north of atwood about two miles uh this is his circular drive he's got pins back there we we operate we rent this from the local vet and then when we're processing our cars park here and we load the chickens in the back from the back end um so they come in this back in right here is the inspector's area he's got a restroom a locker a desk clothing there the chickens load on that backside they come in we use killing cones here's our plucker we have one person here two people working in here and then we hand through here to the eviscerating area we have uh you know the inspector stands over here and the chickens we got you know the legs and cutting the lining and then checking the feathers so you got a lot of checking here and to get that bird into the air chiller so that's how it runs through there and again we're doing about 150 and three hours um the air chill here generally they they'll break for lunch come back and then they can either start packaging or generally we let them sit overnight and and start doing it the next day these this market that all of these chickens are going to is fresh meat going back to dember restaurants right now we and they want three i think it's two and a half to three and a half pounders because then they split them in half and make about two meals out of them anything that's smaller or bigger we freeze it and that goes into our local sales right markets uh benefits uh convenient and efficient uh cost effective easier to access in the usd inspected facility um the challenges probably asking how much it costs to do this i talked about the construction time uh when you're doing it ourselves the regulatory processes and then the funding uh we we thought when we did our original budget it would be around $50,000 it ended up being 75 and a lot of that we we did calculate a value on time and um where we are so that kind of gives you an idea if you were to go buy this already prepared and not go through the that trailer on cornerstone i think i saw of that size was about $130,000 for all the equipment so it does save some um regulatory you know and for us the other reason we we we we kind of do believe that at some point it may grow to where we possibly need a fixed facility particularly um where maybe different but we're covering a lot of areas so maybe it's doing multi-species and that those were so unanswerable at the time that we just wanted to focus on the chicken and then we go this thing could move to another group of producers once it got full and then we then we could work on that so more of the general plan is it will probably move across the state line to one of the other clusters of producers whether it's up in the Nebraska Panhandle or down there close to Colorado go through the same process with the permitting and regulatory and let's say that would take because we don't want to shut down now so once that process kicks in have the other thing up and running so that one can move and and do that type of transition uh so that that's that's was a lot of them when we say mobile it's not going from farm to farm mobile to us was to cross those state lines and do this whole process over again and and and go from there our farms are more mobile I think to do the the farm to farm would be wiser for us to get a do a hub facility that does aggregation and collection and then buy a sprinter vehicle to go to the farms or a trade or trailer if they're live and sprinter for vegetables and go pick stuff up and that but that's part of your you know if you're doing a food hub things to consider um so I mean those are you know you had some of the questions on on those um again then you know our publications and outreach we have a healthy communities initiative in northwest Kansas so they chose to do food as their initiative and they sent all their technical assistant people from eastern Kansas and lawyers from Minneapolis and all that out to watch and tour this when we were processing one day so it's being assimilated through those type healthy communities communities if you're from there's 20 of them in Kansas they have a pretty good idea what's going on out there and would connect with us the USDA employees themselves are talking in and and you know they they like I said are probably receptive of seeing more poultry in Kansas and working working with farmers to to do more of it our high plains food co-op annual meeting this meeting and other other meetings are part of our outreach future recommendations from us that the crew or the co-op that worked on this project um work with your policy councils and your states and USDA if you if you got the poll to go to Washington and start with the secretary down or somehow let's let's talk about streamlining this and planning a little bit ahead so so the next people don't have to take so long or another state and coordination somehow there be honest with the startup funding requirements again it's not a huge investment to do one of the smaller scales but you know be any project you know figure some contingency on that and then be conservative with the market and the customers there's only poultry farming isn't easy and so so be realistic on what you can actually deliver and don't over promise the customer that you're going to have fresh chickens for 20 restaurants when you can only really just work with one to start so in that 2014 we actually with those 600 and what we were already doing piloted with five and then this year we have about 25 customers in this market so that's that's probably my biggest what if you're going to go into the scale up thing and try to go from direct farmers market and that really communicate that with your customer uh they'll they'll understand if bad weather comes and delivery doesn't get out there if chickens all die that maybe for two weeks they might have to pull off the menu but as long as they know you communicate that with them uh the other thing we learned if you do this and there's entities out there that say they're doing this compete against you on the pricing they are raising their chickens in Arkansas or Iowa and locally processing them in your market selling them as local and the quality is not there and those customers will come back so don't lower your price that would be my other recommendation is compete in your market and understand your customer yeah now like I said ours is right now fixed and and and when we when we're if we're gonna we you know if you pull up ser and look at the other projects across the country some of them are you know but then they don't like us we have that state line thing that brings the USDA in a lot of those other ones in Vermont and those are our states and they're run by a university or that and they do go farm to farm to farm so the state the state ones depending on the state if it's approved and they don't the state inspect sometimes the state inspection there is no inspector it's just approved and then it can do it but Kansas and you know we're we're we got an inspection system that we're USDA so it doesn't matter but if if we were to do a mobile in Kansas we'd have to operate under those guidelines and probably not have to have the inspector there each time to the bird so it could save you you weren't going the USDA route but then in Kansas you have to limit if you're gonna you got choose either USDA or Kansas you can't as a farm market both ways and if you would choose the Kansas side your farm is limited to 20,000 that's kind of how I understand it from our regional guy that they would like like they do with your meat license they show up randomly once or twice a year so okay thank you I'm wondering if you did the the figures on how the cost of making this mobile facility would compare to the cost of doing a traditional stationary facility a traditional um we now we have now a all meat type facility I know the last one we toured in Colorado that had the poultry sign that the cream of the crop was 1.3 million if you were just to put up a shed go through the process with the drainage and that you would probably be very close to this same figure um but that you know that would be bait I mean any expansion if you did something on the farm you could probably anticipate around that same cost I was doing your numbers on the chickens for 600 chickens figures out to about 13 33 a chicken yep yep that year that's probably what we are we're selling them for 12 25 those three and a half pounders and then when you raised your production up to what was it 8,000 and just rough figures come out to about 12 50 a chicken or something I would just guess the numbers so how much is your your uh transportation cost on 15 for uh accounting marketing packaging and the transportation you add 15 yeah it's about seven percent for the transportation seven to eight two to three for your internal uh stuff and then the other percent goes back into the co-op for infrastructures uh it's 350 per pound and the farm is taking back about three bucks it's like 60 minus 60 cents 290 something like that per per pound


Another case reported acute toxicity linked to noni juice ingestion, this time in a 14-year-old. At least his liver didn't fail more completely like in two of the earlier cases. What might you expect from a product also known as vomit fruit? The multi-level marketing company that sells noni products blamed aloe vera juice the boy had also consumed, which is indeed something else I'd encourage folks not to drink. But what about all the scientific studies promoting these types of products bandied about on their respective websites? Recently, a public health researcher took the time to review the science in liquid dietary supplement promotion, evidently a $23 billion market. Central to the marketing of many such products is the citation of scientific studies supporting the product's health claims. While these studies seem deliberately created for marketing purposes, their findings and quality are generally presented in a manner that appears designed to mislead potential consumers. Here they use the case of mangosteen juice, another product I've warned about in the past, as an example of how widely marketed and consumed liquid dietary supplements use exaggeration and pseudoscience to bolster their web promotions of product effectiveness and safety. The multi-level marketing company that sells mangosteen cited a study they paid for to support its assertion that their product is shown to be safe at all dosages tested and indeed safe for everyone. The study involved exposing just 30 people to their product, though with another 10 given placebo, as the researcher notes here, if that few people exposed, the stuff could kill 1% or 2% of people and you might never even know. This study of the multi-level marketing product Metabolife had 35 on the stuff, and they seemed to do just fine until it was withdrawn from the market after being linked to 18 heart attacks, 26 strokes, 43 seizures, and 5 deaths. Oops! Hydroxycut was studied on 40 people, no serious side effects, and same story, withdrawn after dozens of cases of organ damage, including massive hepatic necrosis, requiring liver transplants and death. And oftentimes the multi-level marketing study researchers don't disclose their funding sources, pretending to be objective scientists, but a little detective work exposed a whole web of financial conflicts of interest. At best, reducing the face validity of findings, and at worse, they represent deception.


It's 11 p.m. I didn't really get anything done today. A lot of you have been saying how I need to rest. I need to get to sleep. I need to not stay up so late. It's just a little. I don't know how. Anyway, a lot of you have been saying that I need to get some rest and recoup and not stay up so late editing vlogs and stuff like that. Today, I think my body was just like you need to like just lie down, sleep, catch up on sleep. So yeah, I actually got up early this morning. So you go take care of my unemployment situation, which I'll get into after this. So I didn't get enough sleep last night because I also stayed up late editing and I got up early. So by the time I got home, I was like tired and I ended up going in and out of sleep for a couple hours, had breakfast, and then I had a headache and I knew I had to go to the gym, but then I was like, I just had this headache and I felt tired and groggy so I ended up sleeping for most of the afternoon into the early evening. And then because I hadn't eaten lunch, I definitely didn't have energy and I felt lethargic and I couldn't really think straight. And it was just, it just begot more lying around, more not doing anything. And I finally ate around 7.30, 8 p.m. lunch and then dinner shortly after that. And now at the end of the day, I'm like, okay, well I don't want this entire day to be a waste, so I'm gonna get some stuff done.  And then even if I go to bed late, at least I got a good amount of sleep catching up that I did today. And then tomorrow, hopefully I can hit the ground running, get some more accomplished, answer emails, work on these cocktail videos that I'm doing, follow the AHF on their projects, and yeah, just get stuff going. Keep pushing for the competition. All right, cardio time. So I just finished cardio. I'm back now. I'm feeling a little bit more energized and I'm gonna get stepped down before I go to bed, so I'm gonna do as much as I can as quickly as I can before I crash. But I want to say a quick thank you to one of my followers and now friends who I met. He follows my YouTube videos and like my content and he was able to help me this morning, get my unemployment for now to tide me over until I get some income coming in. So that was like a huge burden off my shoulders this morning. I woke up early this morning to take care of that, got it done, and I just realized like how much of a weight that's been on my shoulder that I didn't even realize because I kind of got used to that feeling of like stress and like impending, you know, financial crisis. And yeah, after walking out of the office and having that resolved, I just like felt so much lighter and relaxed and maybe to come to think of it, maybe that's the reason why I was able to relax today and to just like sleep and like give myself the day to just pretty much do nothing. Not only that, but this guy, Chris, thank you so much. Had this gimbal for a smartphone that he doesn't use and he offered it to me because you know, he watches my content and he sees that I'm like, you know, trying to get more equipment and up the quality and all of that. So thank you so much, Chris, for this. This is awesome. I can't wait to bust into it and try it out, see what I can do with it, see what cool content I can create with that. And then also, yeah, one of my recent videos, I posted of me driving in my car with my giant while I'm filming on it right now, but my big Canon 80D microphone on top mounted holding that as I'm driving to get like a street view to show you guys. And then he said he had this 360 camera that he also doesn't use so I can mount this to my dashboard. One side face me, one side face the road and give you guys some cool footage while I'm driving or I can even talk to you guys while I'm driving and not have to worry about steering with one wheel or steering with one hand and then holding this giant bulky camera with the other hand and trying to be safe. So thank you, Chris. Thank you for all your help and thank you for these guys that are, I'm going to definitely get up to good use. Another thing I wanted to talk about is, you know, a lot of my closest friends, relatives, people around me who just care about me, you know, everybody tends to chime in when I'm hustling really hard and tired and going through it and tell me, you know, make sure you get rest, you need to slow down, you need to take a break, you need to take care of yourself, stuff like that. But the thing is, and I understand, I get it. I know the mental aspect of it, but I need to be healthy and take care of myself and all that. I hear it. I agree. I feel it. But at the same time, there's a part of me that knows what I'm capable of inside and has always known what I'm capable of. And it is significantly more than what I'm doing and producing right now. And my capabilities expand and grow over time. And the way that that happens is that I'm constantly pushing myself. It's like a muscle. It's literally like a muscle. I feel like life is like the gym and the more than I've pushed those last reps and go further and further. Yeah, I may be incredibly sore after I may be in pain, but it's only going to lead to growth and it's only going to lead to a stronger, bigger, better muscles, which is just my ability to handle life, to tackle things, to be productive, to be really efficient, to just create on a level that I never have before. I'm doing that now, even just with the daily vlogs. And the amount of workload that I have right now with the daily vlogs and then with 80% of my daily vlogs, with the daily vlogs and then with its healthcare foundation, stuff I'm doing for plus life and then other little side projects going out at the same time and podcasts and doing stuff for Jubilee media and just whatever comes up. That alone, like if this was a year ago or even two years ago, I would probably be having like a panic attack. I'd probably be so overwhelmed. I might have a mental breakdown and like cry and I just know like progressively over time, I'm more well-equipped to handle more and more and that's because I'm pushing myself so hard. That's one point. Another point is I know and I believe that in order to be an outlier, to achieve success on a level that is greater than most people, to be in that top percent, you have to be willing to do and think and say and feel things that most people aren't willing or can't. So when people around me, when the majority of people around me are saying you're doing too much, you need to slow down, you need to relax, you need to take care of yourself. I say that as a good sign that I'm in the right direction, that I'm doing the right thing and to not stop and to keep going because that means that I'm standing out as someone who's working harder than they recognize anyone else working or doing more than what they see other people doing and that's exactly where I want to be. So with all of that said, the challenge is for me to find that sweet spot between extreme growth, pushing myself really hard, doing more efficiently than those around me but not quite going too far that I cause myself to break down, shut down, get sick, down or spiral or any of those other negative health consequences. So it's constantly trying to navigate this. I don't want to call it a tight rope because it doesn't feel like it's that precarious and over time I've gotten better and better just listening to my body and what my body is telling me and going off of that but there is definitely a fine line between really going to the extremes like an extreme athlete and then just being reckless and careless and dangerous with myself and I'm getting better and better at walking that line and that's the goal. So I don't know, that's just a tangent I wanted to go on and maybe some of you will agree, some of you will strongly disagree and that's okay but all I know is I'm the happiest I've ever been, I'm working harder and better and faster than I ever have and I know I have a lot more in me so I'm going to keep pushing and I'm going to you know every once in a while take little breaks when my body cues me into like it did today and other than that I got no complaints.