So, in the last class, I talked to you what is a discrete random variable, what is a continuous random variable and I introduced the notion of probability density function for continuous random variable, then we talked about what, we talked about expectation of a random variable. So, moving on, expectation is one characterization of your random variable, like that gives on in a sense like on an average, what is the outcome I am going to see when I am going to perform this experiment. Other question you could ask is, okay, fine, like this is the average value, but when I do the experiment, it is not like I am going to see some expected value, right, like I am going to see different, different realization taken by the random variable. How these samples are going to be away from this mean value? So, mean value gives some average characterization, this is what, but the actual outputs I got how far they could be, is it that they will be very close to this mean value or they will be very far, how that, so to characterize, we will have another notion called variance. So, as you see here what I am doing is, I am defining the variance to be expectation of a random variable X, but it is kind of centralizing it, like I am looking, removing the mean value from it or that means what I am looking at the variation of its random variable X around its mean, but I am not worried about whether this variation is happening on the right side or on the left side, I do not want to care about it. So, that is why I take the square and then I look at the expected value of this. So, this is called the variance of the random variable. Now, if you are just going to look, expand this value, you are going to see that and if you just expand it, so see here, this is a constant, right, already. What you are removing from this X is a constant value, that is the mean value. So, this is another random variable, what we call centered random variable and then we have squared it and took the expectation. If you just going to expand this, this is going to be going to be this quantity where now we have variance is the expected value of the square of the random variable, what we call it as, we call this as a second moment here because the first moment is my simple expectation. My second moment is expectation of X squared, my mth moment is expectation of X to the power m, like that we will come to that. So, this is the second moment minus the square of the first mean. So, if I give a random variable and ask you to find the mean, that mean can be positive and negative, it can be both, right. What about variance? It is always going to be positive quantity. So, now let us see, okay, we have seen mean variance and one of you asked, let us see like the mean looks like some average quantity, right, but that is not what I am going to get when I perform the experiment. So, what you are often, but mean is still some quantity of interest, right, like it kind of give you the globally what is happening, like what kind of values I am going to observe on an average. But what you would be interested is, okay, if I perform my experiment, what is the probability that my outcome will be larger or smaller than my mean value. So, suppose let us say the height, if you are going to take the example of height of the population, let us say mean value is let us say 5 feet, okay, but if I am going to pick an arbitrary person, it is not necessary that is height is going to be 5 feet, right. But his height may be more than 5 or less than 5. Now you may be wanted, may be interested in asking the question, what is the probability that the sample I pick has a value which is larger than this 5. So, how we are going to characterize such quantities. So, that comes from something called Markov inequality, okay, Markov inequality gives a, I mean it slightly answers a different question that I posed right now. And it asks, what it tells is, if I have a random variable, what is the probability it takes a value larger than a certain number. So, suppose let us say y is a positive random number, then you may be interested in asking this question, what is the probability that y is going to be greater than or equals to c, right. You perform an experiment and you want to know like the outcome of your experiment is going to be larger than or equals to c. For example, let us say you are in a, you are like if you are going to put your money in casino or let us say stock or something, you want to ask at any point, okay, whether my returns are going to be larger than this quantity. Let us say I am going to make today if I put invest in the market, the outcome you are going to get by your investment is a random quantity, but you may be interested in asking the question whether my outcome, my returns are going to be at least like let us say 10,000 rupees, how you are going, so you have this. This is nothing but what, this is the, this is like complement of your CDF, right, CDF is why less than or equals to c, but let us not worry about the equality here. So, suppose you want to, now Markov's analytic says that this quantity is upper bounded by that you going to be larger than this quantity c will be upper bounded by this ratio, okay. So now, let us plug into some value, suppose let us say c is some real number, right. Let us take c to be expected value of the random variable y itself. So, what I am asking, if I do that what the question I am asking is what is the probability that y is going to be larger than or equals to its mean value. This is going to give a value of 1, right, but that has no meaning to me because I know that probability is always going to be less than or equals to 1. But if you are going to ask the question, if you are going to choose this c to be much larger than the mean value, let us say in your experiment y is such that y has a mean of, let us assume 0.5. Now, if you are going to ask the question, okay, what is the probability that y is going to be greater than or equals to 0.5, through this inequality you get a trivial answer which has no meaning to me and which has no extra information to me. But suppose if you are going to set this c to be 0.8, okay, you are going to ask the question, okay, what is the probability that my y is going to be larger than or equals to 0.8. Then this has some value, this is going to be 0.5 divided by 0.8 and in that way it characterizes u being away from the mean value, how fast it is going to be shrink, okay. This is a simple relation, but this is one of the basic results that is useful in many, many scenarios. So, let us try to understand why this is true and notice that I have written this inequality only for the positive random variable, okay. This comes straightforwardly, so if I write an indicator function like this, so y is a positive random variable, all of you understand this notation? This is an indicator notation, right, what does this say, yeah, so if this is, I have defined a random variable like this, it says, okay, you perform an experiment. If the outcome of y is going to be greater than or equals to c, that means this condition is true, right, then it is going to take the value 1. If this y happens to take a value less than c, this condition is not true and this quantity becomes 0. So, it is simply saying that, so what I am basically saying is indicator, so a is an event. So, this is going to take 1 if a is true to 0 otherwise, such a function is called indicator function.  So, here you are going to define this function, let us call this as extra random variable x, what you are going to, so x depend on y in what way, whenever y takes value greater than or equals to c, x takes value 1, otherwise it takes 0. So, here y could be a continuous random variable, it could be taking any value, but now through this indicator function you have defined another x which takes only 1 or 0, it you have a binary random variable which is a function of this y. Now, if I write like this, is this relation true for a positive random variable? Okay, now let us see, suppose y is greater than or equals to c, the left, this quantity is 1. What about the right quantity? Greater than 1. Greater than 1, so it holds. Suppose y is less than c, this is 0, but what is this? Some positive number, non-zero, I mean positive number, right, so this relation again holds. So, whatever be your choice of c, this relation holds, right, so now if I take expectation on both sides, so this is true for all c, I see, okay, so now I am going to take expectation on both sides. If I take expectation of both sides, my claim is the expectations also retain the same, the inequality direction remains the same if I take the expectation, why is this true? Yeah, so we had stated this property, right, when did we state this property? Right, so we said that if there are two random variables x and y, such that x always dominates y, that is x is greater than or equals to y with probability 1, then we said that expectation of x is greater than or equals to expectation of y. We had a name for that property, right, preservation of the order, did I apply it correctly here, okay, so because this is true, probability 1, that means this relation always holds, right, irrespective of what value y takes and for any given c, so this is true and I could apply this. Now, what is this further? What is the expected value of this indicator function? So, if I say this is nothing but probability y greater than or equals to say, is this correct? Okay, fine, so that means that this true, then we are done, right, so here y and c, so from here to here, what property did I use? Just use the scaling property, right, because he is a constant, so that is why we get this. Yeah, if I am going to assume, if I do not assume c is going to be greater than 0, if this become negative, then it may not hold, right, because I already assuming y to be positive random variable, right, it does not make sense to take c negative, because I know that y is, it is always going to be greater than 0 at least, which one, this part, yeah, if I am going to take this is going to be, yeah, right, that is fine. So, this is going to be 1 in that case and this is going to be negative, so it does not make, this inequality does not hold, but fine, we have to explicitly put, if you want to make it correct, okay, so let us say c greater, strictly greater than 0, because otherwise not true, but I mean this, for a positive random variable having c to be negative, taking negative does not make any sense, because I already know this probability is 1, why we need a bound and then the next inequality is called Chebyshev's inequality, so the Chebyshev inequality exactly tells how much, what is the probability that my random variable x will be taking value away from the mean by certain amount, so let me, so suppose if you are interested in asking this question, another thing is often I am going to use sigma square to denote variance of a random variable, so when I want to make specific that this variance is associated with the random variable, I will put x like this, okay, and if I am not specifying, I mean always I do not need to specify which random variable it is associated with in this, I will simply write it as sigma square, for any greater than 0, so to make it then we can write the probability that x minus mu greater than d is upper bounded by sigma square by d square, so what is this basically saying, mu is what, mean of this x and the sigma square is variance of this x. Now if I ask the question, what is the probability that the value taken by random variable a, when I compare it with its mean value, the probability that it will be away, I mean that difference of the x and the mean is at least d, what is this probability, this statement says that this probability is upper bounded by the ratio of variance divided by d square, okay. So do you see in any way like this quantity over here can be derived from this, in what way, how? So this is, I have deliberately put absolute value, right, if it is absolute value, if I am going to take square on both sides, the order is preserved and the probability should not change, okay then. So now if you apply Markov inequality, how we are going to apply, you are going to treat this quantity here as let us say y and this quantity is a positive random variable, right, because this is the squared value. Now what is the expected value of that? So when I am taking square, I really do not need to worry about this absolute value here and what is c? So c here should be what? d, d square, d square. Now what is this expectation of x minus mu whole square? Variance. That is variance and that is exactly this, right. So you see that like the Chebyshev inequality here, whatever I have is implied by my Markov inequality. Now what it is saying? Suppose let us take two scenarios, let us take two scenarios, let us say I have a random variable x with mu and let us say, so let us say I have two random variables, x1 with mean mu and a variance sigma 1 square and I will take another case where I will change this variance to sigma 2 square while keeping mean same, okay. So what, by our understanding of this variance, it should be such that in this case my x, the spread of my x around mean if suppose sigma 2 is larger than sigma 1. So by our understanding vaguely at this definition, the variation is more, right. So if sigma 2 is more than sigma 1, in this case this x should be about its mean value, it should be like spread, okay. So in that way, if I am going to increase the sigma square here, this probability is increasing, right. So that means then me looking at this x being spread around mu, then that probability is also larger, right. So in that way this Chebyshev inequality is kind of capturing how your random variable x spread about the mean value, okay. So we will see more about this when we look into specific distribution, okay fine. So next I am going to look at something called characteristic functions where j is my standard ILS number and this is nothing but, so let us take a random variable which has a pdf, that means x is here continuous random variable. I am going to define its characteristic function as for any u that is given, it is going to be defined like this, expectation of e to the power ju and here x here. So this is the random quantity here, u is fixed, j is fixed, j is your simple ILS number, complex number and by definition or expectation, this is the value of characteristic function, right. So now if you are going to just look at this f of x as some function given to you, what is this quantity indicates? If you look into like Fourier terms in terms of Fourier terms, so you guys recall what is the Fourier transform. So Fourier transform is defined for a function, right, give me a function, I will define the Fourier transform of that so that I can go from frequency domain to time domain and vice versa. So if I am going to treat f of x as my pdf as a function here, what is this quantity here? So this is nothing but the inverse Fourier transform of your function f of x and also there is a 2 pi factor here which we have not considered here. So this is just a definition. Okay, what is the consequence of this definition? Why this is useful? So earlier I told that we are going to say that this is x to the power k, I do not know if this exists or not but this I am going to call it as kth moment. So k is equals to 1 correspond to expectation, k equals to 2 corresponds to the second moment like that. So by the way, if I say my variance is finite, suppose let us say is my second moment finite? So if I say this quantity is finite, variance is finite, it is given as the difference of these two quantities, right? It must be the case that this should be finite, this must be finite otherwise that quantity is not going to finite. So if variance is finite, my second moment is already finite but I do not know like the higher moments will be finite or not. But at least if I say as long as variance is finite, my second moment is finite, you will also see that if your second moment is finite, also implies that your first moment is going to be finite. Okay, fine. Now if I want to find the kth moment of a random variable, then this character function comes handy. How is that? So suppose let us say we have, I know this characteristic function of a random variable x, all I need to do is take the kth derivative of this function and compute its value at u equals to 0, then that is going to give me the kth moment. So I am going to just write it, so this relation holds. So what is this? When I wrote write like this phi of k with a superscript k, that means this is the kth derivative and I compute it at 0. This is simply going to be j to the power k and expected value of x to the power k. So that means this quantity is simply going to be related to the kth moment directly. So you can directly see that, if you have all like this, if you are just going to differentiate this with respect to u, every time you differentiate this with respect to u, a x factor comes and every time second derivative, another x factor comes. After kth derivative, k, x to the power k factor comes and when you plug in u equals to 0, this term vanishes and you will end up with it. Just this is a computation, just look into that. So one good thing about this is, why this is often of interest, the character function is, every pdf has a unique characteristic function. So if you know a pdf function, you already know how its character function is going to look like. So if you know already characteristic function, you also, you can immediately say this character function belongs to this pdf function. So I am going to say that two random variables, say pdf, if and only if they have same or instead of probability distribution have same characteristic function. I think this is slightly stronger than not just pdf, it is going to be probability distribution. So if you have a probability distribution and if you are going to complete its character function, that is going to have a unique one. And if you have a characteristic function, you can associate it with a unique distribution that way. So this, we are going to use later when we are going to do some theorems like. I think we are going to use it when you prove center limit theorem and all. So this is for a case where I have a pdf and we can also define similarly for a discrete case. So for a special case when my random variable is non-negative for a non-negative random variable x, we are going to define z transform which is defined as phi of x of z is equals to expectation of and where I want this region of convergence range to be less than 1. And again we can show that for a, this is for a discrete random variable which is taking non-negative value, again we can show that phi of x1 is nothing but expectation of x, x minus 1 all the way to x minus k plus 1. So here it was straightforward that in the characteristic function, if you take the kth moment and put computed at 0, it was directly related to the kth moment. But here in the zth form for it is not so straightforwardly related. So I am going to, if you are going to take the kth derivative of this function in z and then compute it at the value z equals to 1, this is what you are going to get. And you see that this expectation is now involves all the moments. If you are going to just expand this x, x minus 1 all the way to x minus k minus 1, it will going to have expectation of x to the power k, expectation of x to the power k minus 1 and it will, at the end it will also have expectation of just x if you just expand this. And again two random variables have same probability distribution and only if z transforms. Here in this case x is a discrete random variable. Non-negative, we are just going to say, sorry non-negative I have to say integer random variable.


So an artifact I covered unreleased is now found out to be something more than I originally thought. Damage people, lots and lots of stacked damage. How's it going guys, my name's DPJ and today I bring you another BR3 video. If you do enjoy it, leaving a like really helps out and subscribe if you do want to see more. So the pearl of unethical knowledge, she's an artifact rewarded to you by Collaptrap towards the end of the guns Love and Tentacles DLC campaign. And you can see that artifact on screen now. What this offers is, consecutive successful hits grant 1% increased damage per hit up to 15 times at maximum stacks as an additional 20% damage. So going off what this states like I said in my first video on this thing, you basically get a total additional damage output from this artifact of 35%. 15 stacks at 1% then an additional 20% equaling 35%. But actually guys, that's not how it works. Before we go any further, credit to this find or first to cover this video must go to Moxie. As far as I am aware, he was the first to bring this to the community's attention. So if you guys would like to go and check him out and show him some love, his YouTube and Twitch can be found linked within the video description as far as Borderlands streamers go, in my opinion he is the one to watch. So yes, brought to my attention was his video stating the damage this thing stacks to wasn't what we first believed. It was calculated that this thing in fact actually gives you between 120 to 150 additional bonus damage. Calculations I couldn't find so I decided to try and suss this thing out myself and bring you guys this in a farm even a noob like me would understand. So these calculations may be slightly off but under my testing this is what I found. So a standard weapon at default deals 100% damage obviously. So with that first hit you will see damage equaling at 1.01%. Calculating add that to 15 consecutive hits and you are left with a damage percentage of 1.16 I do believe. So let's say you have a weapon which shoots a standard damage of 11 like we see here within a level 1 infinity pistol. I wanted something lower level to demonstrate and make calculations on to make it easier. So after 15 shots your output would be 11 times a 1.16 and that equals a 12.76 but again won't show such a number so you get either a 12 or sometimes 13 number pop up which we see with the infinity pistol after those 15 hits. So with this damage number in mind we then have to add that extra 20% damage this artifact offers after the 15 consecutive hits and the way you would work this out is as follows. Now what you do is you calculate these two weapon numbers together which would be 11 times 1.16 which equals 12 in game and then we add that to 11 times 1.20 which is 13 in game. Then add the 12 and a 13 together and we get 25 and that's a total stacked damage we do indeed see with this infinity pistol making them all out of this artifact. So to calculate the total damage multiply this artifact offers percentage wise is quite easy. We started with 11 damage we ended up with 25, 100% of 11 damage would take us to 22 damage. Adding the remaining 3 damage percentage wise is about 35% ish give or take a few numbers and that's what it seems we are getting in total from this artifact around that 130, 140% damage increase from consecutive hits. Like I said give or take a few numbers here people it's been a long long time since I did do maths. Now what else is also interesting is when stacking a damage if you use a weapon which shoots multiple pellets or projectiles per shot the 15 stacks happen much much quicker which makes the crazy results with weapons such as the anarchy and you can see this in action with this artifact in action on screen now against grave ward. So yeah people it's a pretty cool artifact and in fact it's an artifact I originally put off due to my initial thoughts on the damages thing that I actually offered. It's great to see that actually isn't the case and in reality this indeed is a top tier artifact there's no two rich ways about it and to be honest guys I actually don't think this is a bug or glitch like many people are thinking I feel this was intended and I wouldn't really expect any kind of patch or nerf to land on this thing I really wouldn't. So yeah guys a quick video clearing this up for those a little confused on the matter I hope this helps you out. So yes people it seems in total the damage percent bonus we get from this pearl of ineffable knowledge artifact is around that 130 percent damage output which is pretty damn cool but on that note guys we have come to the end of the video if you guys enjoyed it leaving a like really helps out if you're new around here want to see more boardlands be sure to subscribe and if you never want to miss a video upload you can turn notifications on by hitting that bell button but guys thanks as always for stopping by hopefully you enjoyed the video and hopefully I will see you on that next one


Morning everyone and welcome to the call to the class today. I've just Started the recording of this class this lecture and We will pray and get started Paul if you want. I know you're it's 330 probably 330 in the morning you can turn your video off fall level 2 if you want to Yeah And Yeah, but thank you for connecting I know it's very very early over there and God bless you God bless you. All right Let's pray and then we will get started and I'm sure this will so in the class in a minute or so All right, let's Invite somebody Brother Manohar would you please like to pray and we will get started Well, father, we thank you Lord for this morning grace to Study and learn from your Lord. Lord. It is a study of your word and Going deeper into the word father or that enables us for the mission Lord as we are studying the subject of faith Father, we know too much about it, but we fail to practice it Lord Lord Don't this impartation of this teaching Lord that whatever we have learned and whatever we know and whatever we hear No in this class. He may implement in our life. Our faith may affect it father Lord as Abraham had great faith Help each and every one of us to develop in the same faith So that we may walk Lord in the authority and the ministry that you're doing to us in this In this in this world, Lord, we come in this class They come in the pastor and everyone who is joined to this class into their hand Lord speak to us father strengthen our Build us up and let us upon a rock Lord in the faith and use us mightily in the ministry In Jesus name we pray amen Amen, amen Thank you Thank you, brethren or and welcome again everyone. Thank you for connecting to the class We started this course on faith last week we gave a bit of introduction and we were still in the first chapter on the introduction just covering some Our foundational aspects on faith and I'm just going to quickly review Some of the things we did last week and then we're going to go forward. I've Shared the notes for chapter two as well as for chapter three We will see how far we get today I'm hoping we will be able to finish chapter two Today and get started with chapter three. So I've put the the lecture notes for both of them in the Yeah, today. I've been having some challenges here with the network Just want to make sure things don't drop off. Okay All right So let me just go ahead and share my screen and we will Just quickly review some of the things we did last week in our introduction so we went through the definition of faith in Hebrews chapter 11 verse 1 we spent actually quite a lot of time on Hebrews 11 one trying to understanding What faith is we mention that faith and I believe they come from the same root word faith is the noun believe is a verb And so we are going to use them almost synonymously As we communicate So we went through Hebrews 11 one we talked about other aspects of faith that faith connects us with God We are people who live in this natural world But our faith in God gives us the ability to connect with him and thereby work With him and experience his work in our lives We also said based on Hebrews 11 6 that faith pleases God God is pleased when he sees us Have faith in him We said that faith isn't the person of Jesus Christ. I'm just quickly reviewing And you're you're welcome to listen to last week's You know lecture videos in case you would need to review any of these things We said faith isn't the person of Jesus Christ So Jesus is the author and the finisher of our faith is the originator and the completer And so faith is not You know some sort of a mind game that we are playing It is in God himself the one Who is the author and finisher of our faith? We also said faith is based on relationships. So it's something that we that develops You just as relationship develops You know as our relationship with God becomes stronger be I'll under I know him better Then our faith in him also gets stronger And so faith is based on relationship. We also said faith is of the heart so many times We believe in God and we believe his word even when it is contradictory to our mind You know, our faith is not always comprehensible To our mind now we can believe God and not necessarily Explain everything with our minds you know, but faith is of the heart and we Our spirit beings we have spirit soul and body and so our heart or a spirit Can believe God even though there are things our mind will never understand And our mind will never be able to explain but faith is of the heart And we said that God calls us to live by faith. That's the way he wants us to I live he says, you know The just will live by faith So this is how we live we walk by faith and not by sight We then also said that faith is conceived and nurtured by the word of God. So The word of God is very foundational We read the word of God It helps us to know God and also helps us to know what he has promised what he said he will do And therefore we believe that and so the word of God is what conceives right then what nurtures right It's the basis of our faith. So we're not just, you know, faith is not whimsical It's not something I fancy and I imagine and I just make myself believe it No, faith is based on God's word God is truth. So everything he speaks is truth and truth Can be relied upon we know truth will not fail. This is absolute we can depend on it and so We trust in his word and then when you have faith in the word It is having faith in God himself because you are you know, you're expressing trust In the one who spoke the word when you trust his word So When we have faith in the word we are saying God. I have faith in you. That's what we are saying So faith in the word is faith in God's when you believe the words and God, this is what you said I'm going to believe it. I believe it. I'm resting my life on this and Your word is truth and that is an expression of faith in God himself And we also said faith is like a muscle It grows as we exercise it So we just keep using our faith right We talk we mentioned about the Thessalonians how their faith was growing exceedingly. So day by day the faith in God increases a faith grows We also said several factors influence faith. So faith needs a healthy environment In which it can thrive and we see in scripture, you know, he says add to your faith All these other things. So word you which is your character knowledge self control perseverance or endurance godliness that is living godly Brotherly kindness and love. So This is the environment in which faith is nurtured. So walk in these things so our faith can grow and faith can be fruitful so we mentioned that and This is where we paused last week at the bottom of page two. Actually, it's the last point But let's start and let's just spend a moment here on this last point and then we will Get into chapter two So what we must understand is that faith causes the power of God and his word to be released when we believe God and we believe his word that In some way and I'm just using this as an analogy. So Sometimes, you know, our our our analogies can be usually to a certain extent. So To some extent it is right to say that faith is like a switch that maybe Faith in God's like I'm trying to switch on so the power of God can flow Right, but don't think that faith is just a mechanism. A switch often represents a mechanism You know, that's what we emphasized earlier. Faith is a relationship. Faith is something that Is based on God's word and grows Right. So but it is true that faith is like a switch that when we connect with God Through faith we are giving God is like at on the switch on so now It is possible for the power of God to flow into my life into our lives and cause Something to happen So let's could somebody read 2nd Thessalonians chapter one verse 11 It's right there on the in the pdf notes that if you're following But I just you know, just good to read scripture. So could somebody read that for us, please out loud therefore we also Therefore we also pray always For you that our God will count you worthy Of this calling and to feel all the good pleasure of his goodness and the work of faith with power Thank you So The apostle paul is praying He mentions different things that he's praying for for these believers who are in tessalonica And I'm just want to focus on the latter part of that was When he's saying we're praying that God would fulfill or God would complete The work of faith With power so When we work Our faith that is when we do something out of faith. So work of faith simply means You're doing something because You have faith Right, so the work of faith So the work of faith He says, okay, I think somebody needs to Um Okay, let me just mute their mic. Uh, okay, I wasn't sure All right, can we all keep our mic and mute so we don't get disturbed. All right Um, we go back here. You do this again. All right. Let's go back. So everyone, please give your mics a mute So we don't interrupt the glass Okay So what we were saying is this The work of faith Simply means I'm doing something because I have faith in God And Paul is praying You You do your work of faith And we are praying That God will complete Your work of faith With power So So obviously he's praying for something that's right Uh, and I know that he's praying because he knows this is how God works What happens when we work out of faith? God fulfills Our God completes our work Which we are doing out of faith With his power So that's what we can expect That when we work out of faith we step out. We're doing something but because the faith in God We can expect God's power to bring that work to completion. The power of God is released when we Step out In faith and let's read a few Most scriptures that's on the top of the next page Uh, somebody could read both these scriptures for us, please Luke 145 and also he improves chapter four and verse 12, please um, okay Let's read those two verses of scripture Luke chapter one verse 45. He bruised chapter four verse two Let's just read again. I'm sorry about the interruption in between. Let's let's do that again, please go ahead Come on. I think they're here. You're gonna read Yeah He uh, Luke chapter one verse 45 Blessed is she who believed for there will be a fulfillment of those things which were told her from the Lord Hebrews chapter four verse two For indeed the gospel was preached to us as well as to them But the word which they heard did not profit them Not being mixed with faith in those who heard it All right, so let's look at these two verses Okay, so the point what it says here Uh, in the last point there is chapter one is that in our faith in God Is what enables the power of God or cause the power of God to release So that's what faith in God faith in his word is so important, right? So when we have faith in God and we work of faith, then it's ours, but we may hear the word But if you don't have faith in that word Then that word that we hear will not profit us. It will not benefit us Okay so Having said that so far now we've just you know covered different aspects of faith Now we're going to go into chapter two And I've put out the chapter two notes in the coursework section And we're going to start, you know Learning about how to walk by faith and how to exercise faith and so on you're going to go into that But now in chapter two we're going to answer uh A very it is it is both a simple question and yet it is some something very profound Uh the question that many people ask and I think Somebody had presented this question in the class last week The question is about God's sovereignty grace and faith and chapter two be are going to God is a grace god of grace and uh He gives to us you know, whatever He gives to us freely by his grace So if God is giving to us by grace really why should we Have faith All right, so what we want to understand today Is how does the sovereignty of God How does the grace of God And us having faith in God how you know, how does all these work together? What I want us to understand is that These do not exclude each other That means Uh, God is sovereign, but God doesn't say hey, I am sovereign You don't need to have faith He doesn't say that As we have already seen God invites us to have faith He says it teaches us you must walk by faith And he tells us look you're you know, I'm pleased when I see you have faith So the sovereignty of God doesn't exclude faith in God doesn't do away with faith in God Neither does grace Do away with faith What we will learn is that God gives to us and it gives to everybody freely by grace But he wants each individual to receive by faith You know, so what God miss available? He makes available to everyone freely by grace but At an individual level he says Or it requires that each one of us receive through faith right so God is sovereign God is gracious And he requires us to have faith So that that is the norm the norm is We receive by faith What God gives freely by grace But then God is sovereign So there are times When God In his sovereignty Can do something out of the norm That he referred to that as the exception. That means Somebody may not necessarily have faith But you know that person experiences Something special from God and that is a sovereign work of God Right and that is God does it because he chooses to do that Right So let's talk a little bit about these three aspects and just you know I've just you know, I've just given you an overview of this And we will tie these together, right? So as far as God's sovereignty is concerned He is ruler. He is master And there are several scriptures that Talk about the sovereignty of God And we will just you know, I'll just read Some of these and these are in your notes App In the lecture notes that we've been given to you in Job 42 verse 2 Job 42 verse 2 the scripture Job is saying I know that you can do everything And no purpose of yours can be withheld from you So Job is saying God, I know you can do everything There's nothing can you can nobody can stop you No purpose of yours can be withheld So God is sovereign. God is powerful and nobody can stop him And the scripture is 115 and verse 3 God is in heaven. He does whatever he pleases So God is in heaven and he does whatever he pleases or God can do whatever he pleases You know, nobody can question God. Nobody can put God in a box and say you know only this is all that God can do And he cannot do these things, you know God does whatever he pleases because he is sovereign So that the scriptures are very clear about and we also must Be very clear about that God is sovereign Secondly The scriptures also tell us that God is a very gracious God Is the compassionate God All right, so again, we're looking at certain scriptures here now.  So who's God?  He's gracious He's Very patient. He's abundant in mercy.  He's a God who's generous and There is no partiality with God, right? So we I've put two scriptures there I stay 34 rooms and rooms to heaven Both the scriptures tell us God is not partial Or there God's no Respect of persons. He does not have any favorites. He's an impartial God So in his grace or let me put it like this His grace is available to everybody equally God is not going to you know offer more to one or unless to the other now God is gracious and he's good to all And he has he's he is no respecter of persons So there is the sovereignty of God is God is all-powerful and he can do as pleases There's the grace of God which is God's generous good God and he is impartial in his grace Now having understood the sovereignty and grace of God It is a wrong posture To state that well God is sovereign God is gracious. So I'll just sit down and just wait for him to You know put things on my life And if he wants to he will do it Now that's a wrong posture What we see the scripture teaching us is We recognize the sovereignty of God He's all-powerful We also recognize the grace of God And every person is given equal opportunity to come to God By faith So that's the only thing he's saying You know we all come on the same grounds that is of faith and On and God rest says, you know, that's the only thing I'm asking all of you Come to me in faith I am sovereign I can do anything I'm gracious. I'm no I'm not partial to anybody But I want every person to come to me in faith That's the only thing and Whoever comes in faith Whoever comes believing God on his terms They will receive out of the power of God and his grace They will receive so This aspect of faith puts all of us On equal ground because God is not a God is not partial So faith really is you know, what we could say it levels the playing field so to speak That means all of us, you know regardless of our background Regardless of who we are We all have to come to God by faith He is a sovereign God He's a God of grace but he says I I want everyone To come to me with faith in their hearts. And so that's what we see in scripture that Both in the old and then a new testament that people Came to him in faith and he responded to the faith That was in their hearts and Where there was a lack of faith It actually hindered him from doing what he wanted to do for people in his grace So God is gracious. He wants to do good things But when there is unbelief He's unable to release the good things to them Not because he he is lacking in grace not because He is weak in power But simply because the people didn't come to him on his terms Which is come to me in faith So We even see in mark chapter 6 verse 1 to 6 And the same things recorded for us in matthew 13 57 to 58. I have skipped down a few pages I'm actually on page 17 there in matthew 13 was 57 58 It says that you know when jesus went to his own hometown his own country He could not do any mighty could not do many mighty works because of their unbelief So you imagine jesus He's been healing. He's been delivering people. He's been doing so much everywhere. He comes to his own hometown He comes to nazar his own hometown And in his own hometown He is not able to do He doesn't do many mighty works not because He doesn't love the people But it says because of their unbelief And you know because they didn't believe this they said hey, we know jesus.  We've seen him as a kid. We've seen him as a young person and Now he's a preacher. Now he's doing all you know He's doing all of these miraculous things and they couldn't open up to receive And so in his own hometown He could not do many mighty works the scripture says because of their unbelief so In this chapter, I just want to impress on our on our understanding that And I'm just going to repeat this and we will have some time for questions Is that God is sovereign that is God is powerful And God is a god of grace He is very generous kind And he's impartial So everything he offers by grace He makes it equally available to every person But there's one thing He's asking all of us to do Which is to come to him in faith So that puts all of us on equal ground And whoever comes to him in faith receives What he offers to us freely by grace So this is what I just wanted to impress on our hearts and minds in our understanding as we begin to go in to study on faith So this gives us the importance of faith We want we need to recognize the importance of having faith in God While we are aware That God is sovereign And God is gracious We are not denying the sovereignty of God That he's all powerful his ruler his king and he will do whatever he pleases We're not taking away from the grace of God that God is a good God a loving God and a gracious God what we're saying is In the Bible God is teaching us That he wants all of us to come to him in faith in order to receive what he offers freely by grace Any questions on that and he Anything she want to discuss on that and I've quickly gone through chapter two but And I know we also had these connection problems in between I'm sorry about that, but You know, let's if there are any questions you can ask you can unmute your mic and ask or type it in the chat and You know, we can discuss this this aspect of God's sovereignty God's grace and our faith Did everyone understand this is it clear? Pastor I have a question Yeah So are the grace that is given equally to everyone? Is it the grace to believe in Jesus Christ as the lord and savior? That's one of my questions and second this Each each of us will be having a different calling, right? So Is this grace talking about the divine empowerment that God Gives us for that particular calling All right, so in in the context in what would be what I was talking When I was using grace, I was talking about God's goodness what he gives to us freely in terms of his Blessing in terms of his provisions into our lives in terms of His work in our lives, right? So the word grace is also used to talk about giftings The word grace in the new testament is also used to talk about empowering for ministry, right? So And the word grace is also used to talk in the in the context of Grace as in character right So the word grace is used in different contexts like if it's used to in the context of Talking about how we live. It's it's it's talking about character if it talks about Manifesting the spirit that it's talking about, you know giftings When it talks about doing the ministry talks about empowering But I was using it in the context of God giving things into our lives You know the provisions he makes the blessings he releases Which includes salvation healing deliverance Financial proficient divine protection everything, you know all of these blessings, you know are Um It doesn't that context that I was using this word grace. So God gives all of this to us freely by grace salvation healing deliverance provision. He gives to us It's a work of his grace Okay, okay. That's no it's good. Thank you All right. All right. See another question Uh, let me pray for someone You know, we should believe and pray respect of the other person's faith What could be the reason for Jesus not doing miracles here with his faith? right So that's a good question so the norm is So when god works healings and it's okay. Many look at the ministry of jesus In the ministry of jesus we see norm An exception and you will learn about this in In the course on healing and deliverance That there is the norm the norm is He ministers or he gives to us like we're saying by his power and his grace And we come and receive by faith So in the ministry of jesus the the norm in his ministry was everyone who came to him in faith He received and in fact the next chapter deals with that What did jesus teach about faith through his Teaching and ministry. That's the very next chapter which we will get into After break and what we will see is In his ministry in the ministry of jesus The norm was Everyone who came to him in faith received Now there were exceptions That means the exceptions were Even when somebody didn't have faith there was a miracle that was administered Like we see in uh, you know and and and okay Lazarus. He was a dead man Jesus raised him from the dead in In the case of the man by the pull of Bethesda that man didn't even know who jesus was But in the case of jesus jesus told jesus fear not only believe So jesus was a man and jesus called him into faith fear not only believe so jesus believed Or in the case of the paralyzed man the four Friends believed you know jesus jesus saw their faith So so that's the norm we see the norm the norm is jesus believed In the case of the paralyzed man the four friends believed and that's why they brought him but in the case of The man by the pull of Bethesda Or the blind man in john chapter nine We they they didn't even know who jesus was And yet he healed them. So that those are exceptions. So those exceptions Remind us that god is sovereign And those exceptions will still happen today But the norm is Everyone must come By faith to jesus Now why does god do the exceptions? Because he's sovereign he will do as he pleases Why does he not do that to everybody? Because he has put a norm in place and the norm is we must all come to him in faith To receive what he freely offers by grace Is that okay? So we must understand these two things Okay, so let's pause for a quick 10 minute break. I once again apologize for the spatchy connection this morning um Hope things will get better We will take a quick 10 minute break and come back and after after the break we're going to going to get into chapter three where we talk about What jesus taught about faith is so the best person to go and learn about faith is from jesus himself So that's what we're going to do in chapter three. See what he taught us about faith. That's a really exciting chapter Okay, so take a good 10 minute break refresh yourself. I'll see you soon. Thanks. Bye now