Hi! Hello, hi! Please introduce yourself. My name is Veri from NewsMay, and we are the professional mini-PC manufacturer, and we are only focused on the mini-PC, especially for some customized ODIM. This one has many Ethernet ports. Yeah, and this one is a very big feature, is a PoE. You see here, don't have the power line, the LAN provided for the mini-PC. The name is PoE. It provides the power for the device. And why this mini-PC has so many LAN ports? It's used the software router. So it's like a Linux? Yes. Linux router maybe? Yes, exactly. That one. Which other most popular product do you have? The 12th generation mini-PC, like this one, the Adelaide P, Adelaide U, 12th generation, and this also... Let me show this back. This is AMD. This one can be AMD and 13th. Here is the 12th generation, 5th, 3th, 7th, and also the 13th generation. One, three, yeah, 7th. Which one is the best? Currently, the 13th generation is the best, selling the most. How much better? Performance? Is it a little bit higher? Yeah, performance is higher and experience is nice. Also, it's the latest CPU. Lower power consumption? 20, 20, 28 TDP. 28. Is the same on this? 28. A little higher? The performance is better. So that means fan less? With fan inside. The fan inside from here, the wind go inside and here is outside. All right. With silent fan inside. Who is your customer for this kind of product? Mostly they use digital signage or use office business use. Do you talk about distributors? Do you talk to distributors here or what is your business at the Hong Kong fair? Excuse me? You are discussing with the distributor from around the world? Yes. Do you make only news may brand or you have other? We do OEM, the local brand. Like in the local have different country have a lot of different local brand. We make OEM for them ODM for them. Is Shenzhen? Yeah, we are located in Shenzhen. Which other product you want to show? I want to show here some feature one, our company feature one. This is also the 12th generation with low power. It's a Cera and a Pentium CPU. I should show you like this. Here is fan less. Nice. And here inside open this one can install the RAM and SSD easily. So take out and open the case. And also have to land calm the two display. Inside have a big here sink like this. This is a here sink. It's specially designed here sink. For the TTP 10 watt is okay. 10 watt. It can do everything on 10 watt. Almost. Almost. Office use serve the internet video everything is okay. What is this? This is actually this device, the case. This one we would like to show how it make the because it's fan less. And with R5S7 how to dispassion the heat. The CPU touch here and by the copper transfer the heat to the here sink here. And then more efficiently with this big copper pipe. Nice. This is a very big heating. Very advanced. Yeah. For the 28 watt. All right. Yeah. Wow. There's never any problem with overheating? Yeah. It's okay. And no issues. Even you are to the aging press and test is okay. So how many years your company do this kind of product? Seven years. Seven years. Always Intel AMD Yes. Never ARM CPU? I'm still currently no. Rack chip or? No Rack chip, no AMD and no no others. Just focus Intel and AMD. How many customers use Windows and how many use Linux? We can say around 18% is Windows and around 20% is Linux and they are professional clients who use Linux OS. Do they make the Linux themselves or you make some custom for them? They make themselves. But we will test with all the Linux OS. It's the latest version. Because you manage everything in terms of the Windows license and people need the license just included? The license it depends on if they are over here, the Microsoft partner they can buy them and send it to us. We have the account in the Microsoft. If they cannot we can provide for them also. And what is this little one there? This one? This is the latest CPU of this 12th generation. It's especially for the Japan and the career market like this kind of. Also the port is very rich port with LAN to display USB 3.0 and also in the front have 2 USB 3.0 and the bottom here can open to install the SSD by hand and support the 256 also. Is there a good price for this? How do you talk about price? People contact you make a big order? Yeah, it's around 100 around for the backbone. All right. And have a lot of colors. Like depends on black blue and also we have the red, green, silver more colors. All right. So then Windows license is more expensive than a mini PC sometimes. Yeah, it depends on the CPU. In the Microsoft license depends on the CPU and the configuration. All right. That's why Linux is a good idea sometimes. Always. Always. Yes. It's free. All right. Cool. What's going to happen in the 14th generation? 14th generation is coming and we will make some models like this one. Maybe like this? Yeah, this is a socket CPU and we will already designed to make the 14th generation CPU. All right. Yeah, this kind of device especially have the rich port in the front and in the back. A lot of display. And this is USB 3.2 generate 2. And a lot of top C. This top C is the speed is 20 gbps. So when you say 2 gen 2, that means also 20 gps on this port also. This is 10 and this is 20. Top C is 20. 20 gps and this is 10. That's high speed. Yeah, high speed for the data transfer. But it works on the 13, 12, 14 generation. Yeah, this one is 11 generation and this is 12 generation. This is 13 generation. And we are also designing the 14 generation.


On the 11th of January for Britain held a hugely successful activist day. I was so impressed and so delighted by such a great day and I want to thank everyone involved in organising that day and of course everyone for attending and it gave us a chance to come together again as a party which I always loved doing.  Please give it some serious thought. We are now taking the message around the country so I will be visiting the regions and we will be looking at your region specifically where good seats might be for you to stand putting the right candidates into those seats and getting our campaigns underway. We'll be coming to your area please do give us a shout at enquiriesatforbritain.uk to find out where we are and when and to express any interest or ask any question about becoming a candidate for us this May. We know we can win and as a tactic as a political strategy this is the right one for our party. It's a chance it provides us with a platform it provides us with a reason to speak to the press and we do really well across the country and we beat all the big parties at local level. So let's grab these opportunities with both hands and make the absolute most of it. We know we can win and we will. It's also the best thing you can do for the country. Standing for election is a really it's a life experience it's a really empowering experience and our candidates always enjoy it. It's your chance to put a truly pro-britain party on the ballot paper and give the British people that choice. Let's shake things up a bit because democracy happens in so many different ways. Street protest is the heart of democracy freedom of speech writing articles blogs it's the heart of democracy but what it all comes down to in the end is who is in elected power and that happens at the ballot box and it's in our hands the ballot box is still ours to use to fight for our country. Get on board get in touch any questions or concerns you have we'll address them and we'll support our candidates every step of the way. Inquiries at forbritain.uk. Let's fight back for Britain. Thank you.


Hello everybody and welcome back to the C++ SDL video tutorial series. In this video we're going to move on from the simple initialization program that we had in the last video, in the last tutorial, to something a little bit more, something that will actually do something. It'll still be very very basic and very very minimalistic, won't really do anything at all, but at least something will happen. We're going to create the basic window. Now let's hop on over to our documentation because that's what we're going to learn most of the things and remember that's online at libsdl.org. That's the SDL's library's homepage. You can find the documentation at wiki.libsdl.org. It's just the preceding term wiki. Okay we were looking at initialization and shutdown in the last tutorial. Now we're going to head back to that API by category, a little quick link over here and scrolling down from the basics. Now we want to look into video and we actually want to be able to display things. We can view information and functions related to display and window management. If we want to create a window, this is a pretty good place for us to start. Now this category contains functions for handling display and window actions. So we've got some stuff here we can do, we've got some structures, we've got functions and whoa! There's a function called SDL create window. I wonder what the heck that does. Let's go ahead and click on that, sorry and let's see what this does. This function will create a window with the specified position, dimensions and flags. Okay so it's got a specific syntax and it looks like it needs the type SDL window because that precedes the function call and it takes a pointer. All right it uses the asterisk and refers to this could very well be a pointer. Okay that's good to note. It takes a string or a constant character away for the title. I guess we can actually specify the title. It needs an x and a y coordinate as to where it will start on the screen. Oh and it takes some integers width and height. So we actually know x and y and width and height so we get to know how big the window will be and flags. It looks like okay it display it explains all this in the function parameters. The x position of the window can be a centered position. It looks like SDL has a flag for that or SDL window position undefined. This must be if the display manager will set the window wherever it wants to be all by itself. It lets the display manager handle that. Looks like there's another variable for that for SDL window position y in this case. We have the width of the window and the height of the window and zero or one or more SDL window flags that can be ordered together or use that pipeline like I mentioned in the last video. Return the window that was created or return null if it fails and you can use SDL to get error function for more information. Here are some examples. Okay cool they've got kind of the same code that we do. Okay it declares the pointer or the window variable is going to be containing this initializes SDL just like we had except we use everything rather than video and it creates this with all these arguments here. Window create window it uses it undefined and we'll probably do the same thing to start with and they're using the window open gl flag but we know we can use more than that and they actually test if the window could not go very well for us and then it will display nothing. It'll actually just tell us could not create the window. Let's do that in our code just to be safe and oh it uses SDL delay. I wonder what that does. It looks like the common here. It pauses execution for 3,000 milliseconds or just three seconds and then we'll destroy the window. Oh that must be a function pretty similar to SDL quits. It must clean up the memory out of location or whatever the case may be. Now it goes on to tell us that the flags may be any of the following or together. Oh we can set the window to be full screen. We can use resizable. Resizable is good. We should use that and okay open gl. I want to see what more that does. Window usable with open gl context. We probably won't need that. We do want some decorations though. Those are good options to know that exist though but I think the only one we'll actually want is window resizable in our case.  Let's check out what that does. Use this function to destroy window. Oh okay. Not much else there. Probably good practice to include at the very end of the program anyway though. So let's head back to that initial kind of example and let's base our code off of that. We can have an SDL window. Remember that's a pointer. I'll name the variable window. Let's declare that variable and now let's go ahead and set it to be something. Window can equal sdl underscore create window. Remember we're using that same naming convention for all the sdl functions the acronym underscore and the camel case function name and we want a title.  Subscribe. And now we want the x and y coordinates. Well they're using sdl window position undefined so that that way the display manager can actually determine where it wants it to go and I'll do the same thing for my code here and I'm actually just gonna kind of layer these so it's a bit more readable and my screen doesn't have to go all that far. Now we want the window width. I'll say 400. Just put a comment here window width and 200 comment here window height. Okay cool. And for the flag let's go sdl window underscore. I believe that's how it's formalized. Yep sdl underscore window underscore resizable underscore resizable. Cool. That's good. That's good for us. And now we can now that that's displayed. We do want to remove it or delete it. So let's go sdl destroy window. I think we just pass in a window. Check it out in the example again. That does just take window there. Okay and they're using display. Sorry delay to be able to see it. Let's do the same thing. Remember to end all of your lines with a semicolon. We'll use 3000 just as well. In fact let's go 5000. So you have those many milliseconds and let's test if the window is equal to null. Then we should display something the screen. So let's actually go ahead and include iostream. We're gonna using C plus plus typical output method output stream. There was an error initializing. Initialating initializing. Okay I've completely butchered this word initializing. There we go. The window. Let's include an end line. And let's go ahead and include sdl get error. Because that was the function that they mentioned would return anything bad. Let's go ahead and search what that actually does just so we know sdl underscore get error sdl underscore get error. Search for this. Okay cool. We get right to the page. Use this function retrieve a message about the last error that occurred. Well I don't really see this happening too often and just in case we do see an error. But let's test if we get a problem just by including that. Okay good. I believe our code is just about fine now. Let's help over to the terminal try and compile this. Right now the file is still called initialization.cpp. I'm gonna go ahead and rename this. I'll use it 01. I'll call it 01 basic window.cpp. And just for housekeeping sake I'm gonna go back to the initialization function and remove all this code. Now I'll go back to basic window. Okay cool. Now I'll hop over to the terminal c++ or g++ 01 basic window.cpp and remember to compile with c++ we use our backticks package config cflags and libs for the library sdl2. Run this. No errors. Awesome. Now let's run this eight on out and whoa I got a small little window here. You can see it says subscribe that's the window title and it displayed for five seconds and you could just see that it was it removed it destroyed the window right after those five seconds. I can move this around just a black box very very simple but if I do nothing it'll close out of it. Cool. We can of course change this to be anything we really want. We can have a delay for only one second. Now if I run this code I'm gonna compile it run the code one second and boom it's gone. One second again and it's gone. So that's how the sdl delay function will work. It just simply delays the processing for however many milliseconds you'd like and the create window function will create a window destroy window destroys it and you have a specific amount of flags that you could use also window position undefined window position centered. It's a good idea to take a look at the documentation so you can really see what's going on and what other options you have for your create window function. Cool. Thank you guys for watching this video. Hope you enjoyed this and be sure to look at the documentation and see what more cool stuff you can do. See you in the next tutorial.


Thank you very much and good afternoon to you all ladies and gentlemen. It's a pleasure and honor to be here I have spoken here before but not on this subject and frankly. I never thought I would have to speak about this subject, but okay Here we are We are entering I think a new stage in the discussions with the United Kingdom about The preparation for the referendum on membership of the European Union We have recently completed a round of discussions with each other member state individually, so we are beginning to have a pretty clear idea of the positions that governments across Europe are taking and We have the letter From the British Prime Minister to the President of the European Council of the 10th of November which sets out the British governments Negotiating points and issues and We are assisting trying to help in the process of Resolving those issues so that the British Prime Minister can call the referendum and we hope That the British people will decide to remain in the European Union and Then we can remain united in the face of the very considerable challenges facing Europe at the moment We are of course well aware and I think this is the case the length and breadth of Europe of the particular implications of all these debates for this country With its geographical economic historical ties to the UK The Irish government its officials its diplomats Spare no effort in telling us that And no doubt are telling their counterparts in European capitals that as well And I think that in London and no doubt in Belfast in Cardiff and Edinburgh too People are well aware of that Irish voice Coming across this is ultimately a domestic decision of course for the British people the Commission will not campaign foreign governments will not campaign but There is no doubt that the rest of Europe has a very very major stake in in the outcome of the referendum To what extent this Negotiation and the four categories of issues which the Prime Minister Sets out in his letter will be decisive in the referendum when it comes frankly, nobody knows I think it's well known and you have a lot of experience in this country that in referendums People sometimes answer the question sometimes bring to bear on their answer to the question other issues And therefore the outcome of a referendum depends to a certain extent on the circumstances at the time Of the vote and we don't know when that will be And and we don't know whether these particular issues are All the fundamental preoccupations of the British people nevertheless, we have to take at face value What the Prime Minister tells us these are the issues that he wants to be resolved and They break down into four general categories Which are the relations between The euro countries and the non euro countries within the European Union and what is called economic governance The second issue is called competitiveness the third sovereignty Essentially the notion of ever closer union and the role of national parliament, so I will return to that and The fourth issue which we think about as free movement and welfare, but is called by the Prime Minister immigration Which we tend to use more generally in thinking about What happens between Europe as a whole and the rest of the world and not movement of people around the European Union the movement of citizens of the European Union now Some of these issues are easier than others which of course means that some are harder than others some are particularly difficult and We don't have a great deal of time If the referendum is to be held in 2016 Time is rather short already But the referendum may be held in 2017 that is the political commitment by The Prime Minister by the end of 2017. There will be a referendum. I think it's well known that 2017 is not a easy year in European politics. There are general elections in France presidential presidential elections in France federal elections in Germany and The United Kingdom happens to hold the presidency of the European Union in the second half of 2017 which would be pretty hard to conduct If you had a referendum in the offing with civil servants Operating under perda rules unable to advise their minutes Perhaps actually ministers would do very well without advice from civil servants. Who knows We we overestimate our importance, but It it would be tricky So we'll see the only thing we know for certain is it will take place by the end of 2017 the legislation calling the referendum is Pending before the houses of parliament in Westminster And there are great debates about for example the voting age should the voting age be reduced to 16 So should 16 and 17 year olds be allowed to vote as they were in the Scottish referendum But have never been allowed to vote in a nationwide Election or referendum before There are all sorts of arguments about that I Frankly shudder to think how I would have voted on anything at the age of 16, but I was a particularly immature teenager no doubt. They must have changed over the years although Won't go to that but the There's a fundamental problem in That we don't have an electoral register with the 16 and 17 year olds and unlike many other member states But perhaps not unlike this one. We don't have Identity cards and a national register of everybody which makes it very easy to find the 16 and 17 year olds We have to go out and look for them advertise The existence of this possibility To join the electoral role the electoral commission will no doubt require a certain period of time for all that to take place This could be a delaying factor In the referendum if the House of Commons accepts the amendment of the House of Lords and this becomes law So there are all these issues which are still a little bit up in the air and before the legislation is actually enacted we will not know exactly The circumstances of the referendum we know the question. It's no longer. Yes or no, but it's remain or leave That was also the electoral commissions Doing and the House of Lords and amended the bill accordingly and the government has said it would accept that in the House of Commons But we don't know the electorate and we don't know the timing obviously The first issue euro and non euro We have had in the last couple of years the experience of creating the banking union the banking union which today is Co-terminus with the eurozone so only eurozone members are part of the banking union But it is open to any others who want to join and creates a supervisory mechanism in the European Central Bank and a resolution mechanism for banks and and other Relevant financial institutions in the course of those very complicated negotiations in which I was involved we faced the difficulties of How do you build something for essentially the euro area alone? within a single market Which today includes nine Countries which do not yet have the euro as their currency and we found various solutions. No discrimination provisions were written in We faced the problem that there is no euro area budget So the euro the only the EU budget, which is the only one we have can be used for certain purposes Even if those purposes relate solely and exclusively To euro area or banking union business and we found solutions based on pro rata compensation in that context those Rules that we found and arrangements we found can be codified of course into a set of principles governing relations between the euro area and The member states which do not have the euro as their currency so I think that That is an area where some constructive work is perfectly Possible building on what has already been done And with goodwill on all sides, and I've no doubt that it exists We should be able to Set out a body of principles governing the relations between the euro area countries and the others The British outlook on this And the British have become fervent supporters of eurozone integration Is that the eurozone is bound to integrate further what Chancellor Osborne calls the inexorable logic of the single currency and That therefore there will be a deeper integration among the euro area countries That is after all the thrust of the recent five presidents report on which work is now beginning And it is also the outlook of the British government of course that the United Kingdom will not join it And that therefore this is a an issue which will continue to be important And that importance is enhanced by the fact that the city of London is of course Europe's major Financial center and it happens to be situated in the country which is saying it's not going to join the euro or the banking union so That is a first set of issues of considerable importance perhaps not on the doorstep in in Democratic Politics in election or in the or in the referendum, but obviously important For the financial sector, which as you know plays a very important role in the in the British economy The second and perhaps the easiest of the four categories is competitiveness where the British government Wants to see things like scaling back unnecessary Legislation supporting economic growth and by the way acknowledges that the new European Commission under President Jean-Claude Juncker is doing exactly that and a lot of this simply I think Requires explanation and communication about the new focus of the European Union on growth and jobs The new trade strategy that we set out a few weeks ago, which the British government welcomed and the commitment to the European Union single market with It's free flow of capital goods and services as the British letter says to which of course we would add people and workers But I'll come to that in a minute. So Competitiveness is something who could be against it after all that Is I think An issue which does not require new measures new legislation It requires just a lot of hard work in doing all the things that we should be doing and say that we're doing and have been doing And making them as effective as possible in the EU centrally and in each of its member states The third issue is called sovereignty Is divided into three? Subcategories the first of which is the notion of ever closer Union Now ever closer Union is an expression which has been used in the European treaties from the very beginning in our accession treaties And is still in the EU treaties today It is not a Legal basis for integration measures It is not in fact a legal basis for anything It is not a commitment to relentless Further integration between states and governments It is a commitment to ever closer Union among the peoples of Europe. And as I said earlier In in your parliament the best demonstration I've seen of ever closer Union recently was English football fan seeing the Marseillais at Wembley last week That's ever closer Union among the peoples of Europe a sense of common destiny challenge And solidarity but as British ministers Remind us in the UK. It has come to mean something else It has come to be associated with what I say it's not Which is a relentless drive to further integration and therefore it needs Modification explanation It needs to be reconciled with the British position which is one of Having already today a whole series of special Statuses inside the European Union no Schengen no no euro opt opt-out mechanisms for Justice and home affairs and so on you can make a whole list of British protocols and special rules all of which is Compatible with the notion of ever closer Union among the peoples of Europe that is a fact today but that no doubt can be explained better and The European Council the heads of state or government of our member states Can no doubt find ways of Making that abundantly clear The role of national parliaments is the second of the sovereignty issues and this has been a long-standing Discussion in European politics over the years how should one Bring national parliaments Into the European public debate and into the decision-making process Without in any way undermining the role of our common shared European Parliament Here the idea seems to be that if a considerable number of national parliaments Object to a proposal on subsidiarity grounds Something should happen how many and what that something should be will have to be a subject for Discussion, but it seems to us very likely that if a large number of national parliaments doesn't like a proposal because they think it is Incompatible with the notion of subsidiarity It is very likely to follow that a large number of national governments will take the same view so perhaps the focus should be on what happens in the Council of Ministers if That happens and that is what we are beginning to think about and I Think it should be possible to find some suitable arrangement the third Sovereignty point is the UK Will knee I quote will need confirmation that the EU institutions will fully respect the purpose behind the JHA Protocols in any future proposals dealing with justice and home affairs matters. I don't think that should be very difficult I'm sure the EU institutions will and do respect the purpose of and certainly the wording of the Protocols in this area. What lies behind this is concern about the choice of legal basis for certain Proposals and there has indeed been recent Litigation in the Court of Justice on these matters, but I think the necessary confirmation and reassurances should be possible That brings me to the final basket as we say a category of British requests, which is Entitled immigration and we think of as I said as one of free movement Now what has happened in the last 10 years or so is That in several member states including the United Kingdom there has been a large influx a largely Unpredicted I have to say of Workers from other member states as a result no doubt of the recession and labor markets responding in the way they do and There's no point in hiding it as a result of the enlargement of the European Union The fact the United Kingdom and Ireland I believe did not use the seven-year transitional period To delay the entry into force of free movement whereas Many other member states did therefore creating some sort of displacement effect now why people move from one country to another and you Irish have considerable experience of this often tragic is Made up of many different motivations People move for many different reasons The question which the British letter asks us to focus on is whether What is the role of incentives created by? Social security systems and The focus of mr. Cameron's letter is on The role of in-work social security benefits as they operate in the British system in particular in respect of low paid service sector jobs where Incomes are essentially topped up by a combination of different social security benefits Which by the way are being merged into one so-called universal credit system in domestic reforms taking place in the UK That's relevant because the UK itself has a moving target of Social security reform going on at home at the same time as it is seeking to marry this to the European system in this complicated political climate so the question is Put by the letter can foreigners be by which is included non Well other citizens of other EU member states can foreigners be obliged to wait four years before having in-work benefits While the British worker alongside them in the factory in the office wherever it is doing the same job paying the same tax Has immediate access to those benefits that looks very like discrimination and Therefore poses very serious problems under the single market rules which proscribe Discrimination in respect of good services capitals and labor capital and labor So we have a considerable Political and legal Task ahead of us in the discussions with the British and that certainly came through in the discussions with the other member states about how you can Run your social security system In a single market the basic rule in the EU is very simple member states have their own social security system Then they make their own social policy choices but once they've made them they apply them to all EU citizens in the same way That's What we have to find a way of doing of reconciling. I can't pretend that that is easy I think in fact it is the most difficult of all these issues Let's assume let's be optimistic for a minute and assume that we find answers to all of these questions put by mr. Cameron What form will the answers take The European Council will I think be the forum in which the resolution will be found So where the leaders all come together their next meeting is on the 17th and 18th of December which in Brussels time is tomorrow When you consider That we have to give them papers in advance that they can look at analyze Talk to their advisors about and so on so on perhaps talk to their parliaments about before coming to Brussels So that's a pretty tight schedule. And as I said, we don't have answers to all of these questions today the next European Council after that scheduled is in February and I have to say my hope is that at the very latest then we reach a resolution enabling mr. Cameron then to Consider announce the date of the referendum and then the campaign proper in the UK will start and The legal form this will take depends on the content that you want to put into it Some people say to us Will there be a I'm anticipating the questions you'll like to ask me will there be a new treaty Well, there certainly won't be a new treaty any time soon European treaties take a long time to negotiate They then take often an even longer time to ratify and to bring into force And I have to say that talking to Our colleagues across Europe. I don't sense any great appetite to embark on a great treaty change exercise immediately Given all the other challenges facing Europe and its leaders at the moment I come from a city which has been on high security alert essentially locked down for the last 72 hours And that's only one example of the dreadful challenges we face something again. I never thought I would see so We will have to see Precisely what the heads of state or government in the European Council can agree amongst themselves by way of Decision that decision may well be in the form of an international agreement between them So an internationally Binding legal agreement between them to do certain things We have had experience of in the case of both Ireland and Denmark of Dealing with particular national issues albeit in a different context by A decision of the heads of state and all government in the in the European Council Will European legislation be necessary? Can't be ruled out It takes a long time can take a long time And the Commission can only propose it. We are not masters of the final outcome Nor of course our ministers in the Council because legislation also requires the full Participation and co-decision of the European Parliament. So that is an unpredictable Process both in time and in content To give you one example of where legislation may be needed and I should have mentioned this perhaps And this will be my last point another of the welfare issues raised by the British government is child benefit Child benefit in Europe today under European regulation is paid by the state To the parent worker wherever the children may be so I am working in Ireland I'm entitled a child benefit. I get the child benefit because I'm working in Ireland And the Irish do not Ask me well, where are your children? They may be here or they may be back at home The British government says that's unfair. We have lots of Eastern Central Europeans Working in the UK Some of them leave their children at home for various reasons. It's far cheaper to raise a child Back there than it is here. So why don't they pay? Romania, Bulgaria, Poland, wherever it is. Why don't they pay the child benefit not us? That's I don't think likely to be popular acceptable At all a possible compromise is an indexation system. You apply a waiting factor. You say I'm the British worker here in Ireland. I go along to get my child benefit. The Irish say where's the child? I say it's he she is back in London. They say well London very cheap to raise children in London We look at yes, we look at Some pre-agreed form of statistical analysis purchasing power GDP whatever you want and we apply a percentage to it That's possible There are all sorts of problems with it Complicated the numbers frankly are not enormous the administration of such a system would not be easy They would have to be constant reviews as the Relative GDP or wherever it is purchasing power parities changed But it could be done that would require legislation we could not saying we will we could propose it, but it wouldn't be ready In time I think before a referendum whenever a referendum took place. So We will find ways to do what The leaders agree that they want to do and our hope is that To a sufficient extent the British Prime Minister's hopes and requests are met enabling him to campaign for The United Kingdom's remaining in the European Union and we also hope but we have no control over that And I don't even have a vote because I've been away too long. We hope that the great British people will vote to stay in the European Union and that all the Predictable and unpredictable Consequences of the other option do not need to be faced. Thank you


Everybody forced here up in six box F1 mixer 2022 Chrome hobby and light so three of each in this mixer. There's your results. Let's get started everybody This next race is this weekend Because there wasn't one this week Here we go y'all good luck. We'll start with four or three light boxes. Excuse me three and three I'm excited to break some allure though It's an alluring product They gotta wait two weeks You think they would just go to like the next place Refractor Marcus Armstrong F2 and then again is that one raising it's not very efficient with gas Armstrong for a He-tech mini diamond total wolf there he is Mercedes 98 of 299 So who are the new F1 drivers here piazzaree and Sergeant the USA orange red il wassa for Dom's So American drivers be him and Mick now, right? Sergio Perez black-and-white ray wave Hmm We're stopping there Yeah, sure It'll be big next year and products Fit the Paldi refractor shirts and a purple friend of Alonzo for Alpine 213 of 299 is anyone gonna top max this year black-and-white ray wave red bull never stopping extra stopping Max for stopping a red bull black-and-white ray wave Again So what's up everybody we watch tonight more WBC more America sadness Refractor Fando Alonzo Alpine fishing is just Bosch young black-and-white ray wave for a compost nugget spin I guess lost a couple not great games recently refractor Fernando Alonzo for Alpine Work at the night epsilon same checkered flag Reno sato virtuosie Toon Town, I've heard that before what is to town? Gold wave of Daniel Ricardo McLaren Grand Prix winner Italy 35 out of 50 Do you see like a Yu-Gi-Oh video game for something but it was like just like the card game There's so many Refractor asked about okay. Did I just want blue eyes white dragon dark dark magician. I Forget what else were the cool cards When I was a young lad Purple Richard for short F2 Tredent 399 from Garoppolo to the Raiders orange red military Botas Alfa Romeo Carlos signs black-and-white ray wave for Ferrari Just because we don't get Black-and-white ray wave in alto for Ferrari Refractor Landon Norris McLaren Someone put up a service for it. I was I was gonna say absolute I was like tune down like something from like my childhood. Yeah Yeah, first time opening allure this year is allure refractor Daniel Ricardo McLaren It seems a bit different from years past though purple checkered flag Kimi Reichenan for Alfa Romeo 39 of 199 Who retired for that one was it just a battle refractor makes Schumacher Haas Right Legals in chat now Black-and-white ray wave best of all no con for Alpine Stop illegal been a minute Pink ray wave here no Ricardo. That looks pretty cool with this helmet there 58 is 75 make a layer in Fractor Lewis Hamilton former Sadie's Checkered flag no block for MP black-and-white ray wave Fernando Alonzo Alpine Last light box that we're into hobbies Black-and-white ray wave Dennis Hauger For Prima do illegal I woke up and after I woke up this morning illegal text me that I need to make my fantasy pick Did everybody pick super quick let yesterday illegal refractor max for stopping Red Bull and a purple Ricardo now same card as the Pink ray wave earlier from McLaren 390 now getting like almost helmet color matches all over the place with that thing Because I picked Mara field like last night and then all of a sudden it was my turn again Apparently had to reset the clock and I was like I didn't even know Black-and-white ray will declare I didn't expect it to be fair for Ferrari. I dropped the ball Gold ray wave a sewer for Alfa Romeo 47 to 50 Not ray wave a gold wave refractor Oscar Piaz Street for Not Prima. I didn't realize this is my thing. I would have you know, I pick right away. I just didn't realize my pick Went to bed woke up and you were like, oh, yeah, he had to reset the clock. I was like what? We have we had a running timer started off at 12 hours and we switched to eight hours after like the first five or six rounds So like we started we started the Saturday before this past one I mean, it's good because everybody has everything going on. I prefer the long draft plus it gives you more than like a Minute to think about what you want to do Perez refractor for Red Bull You won't get you won't if there's like it connection issues won't auto-draft some guy on IR or something Or the IL I guess in baseball refractor Joe rookie for Alfa Romeo. Oh Well, I picked as soon as you texted me I was up early today many diamond Lando Norris McLaren to 60 of 299 nice Lando Purple green Kevin Magnus in for Haas La Clare black and white ray wave for Ferrari tailpoor sharp future stars refractor ART Hey Heather, how's it going? checkered flag you use to nota for Alphatari, but yeah, the puns are horrible Illegal with all the puns Jack Duhan future stars black and white right away for virtuosy I don't even know who you picked illegal. I didn't check today.   I took glass now. Hey glass outside is massive though That's not a bad idea Oh Dude, we could break on the road Gold wave auto Ralph Poshung for Campos Almost sounds like a heart. You know, it's just a B 17 out of 50. It's like Jordan Love without the J It's like glass now See there's a pun already There's a pun already Saudi GP. I might have to watch it. Oh, we got a crazy pack here a checkered flag Lando Norris McLaren orange red Sergio Perez Red Bull Speed Demons Latifi and a printing plate As Lewis Hamilton That is the Lewis Hamilton portrait as well, right? Is that the number one? Oh number eight that's still sick congrats to uh, Mercedes Auto is not much of a signature. It's more of just like a letter That's an awesome plate. There you go Mercedes. We'll get that mag for you. That's a really good plate Yeah, not the best out of but hey, it's a gold wave auto nonetheless. So congrats to that spot Bullock Bashi Saroo's refractor I mean, that's yeah, I still when I talk about like very rarely that's what I do because I don't I'll cut my knuckles on that thing Checkered flag Vettel. I'll still use that thing obviously to get the tape off and then I'll just break the tape and put it all around Checkered flag Vettel. It's more efficient. I think if you're like doing triple threads or something Yeah Purple checkered flag Sergio Perez nice card red bull number and seven of 199 007 I do pull a lot of Lewis Hamilton one-on-ones, don't I Maybe not a lot.  Sam Donald became a 49er. Oh boy Refractor Charles Leclerc For Ferrari That's a big move for them. That defense is still nasty Yeah, we kept Jonathan Jones two year 20 mil. That's good. Yeah, that's good Many diamonds Sebastian Vettel 182 of 2.99 I like Johnny, but they never used him correctly I'll do They probably have like 10 probably 10 targets I mean, they just don't know like screen pass. Yeah A Monza There we go case hit Italy Monza. It's random to everybody at the end Art de Grand Prix Yeah, bon whose birthday is it today? Refractor max for stopping Orange red jq's for van emmer sport Ron baller Tristan Thompson Future charger fractum rino sato virtuosi Crown baller got no range, right? I know we did he he got what the mabs, didn't he? Only time the mabs got a ring All right, two more hobbies There's a jack queen. There's a jack queen now a lot of you jack. There's there's a jack queen on the savers I don't like that at all jack. He's queen. He was jack. Quinn. Yeah, man. I'm telling you It's like top 10 pick purple versus stopping ground. You win another lens to 3.99 Red Bull Landry shaman, I'm gonna go with Koran Butler Because he because we were talking about Gilbert renas last night and he wasn't involved in that And maybe refractor Liam Lawson for carlin a gold checkered flag pierre ghastly Alpha sorry He's pierre 48 out of 50 How reminds you of deputy travest jr. Fractal Lewis Hamilton a gold auto Frederick vesti two two boxes two gold autos for hobby for art six of 50 Yeah, we were just talking about donald and then mike white to the dolphins. I bet Sean has pumped Was he here today? Here to get like new tires and stuff for his car mini diamond George Russell Mercedes 229 of 299 Checkered flag Nicholas Latifi for Williams refractor Lewis Hamilton Mercedes What is up with the camera dude just focus on the card do your job Like bill check out here do your job refractive alterry botas alpha Romeo Yeah, I think we've all been waiting on the rogers news to be official for like what the whole afternoon basically Yeah, I think they said on like Friday like he's not going back to the package. So He'll go to the jets He said the packaging gets on the form Purple target flag Sergio Perez driver of the day, Portugal Number 89 of 199 is Jordan love season. Just about guys. It is Jordan love season season There's gonna be people buying up both trailance and um Rock pretty cards future stars refractor Juan asani. Who's gonna be right? I don't know for domes Seems like it's gonna be a good old competition Sergio Perez refractor red bull Even though if someone said I was originally a long-term that makes me skeptical still Maybe they just got the Orange red you see no to alphatari Yeah, because obviously it's different. He's not throwing as hard as like a picture would Motion isn't as violent He throws in six weeks It makes me worried though for a guy that obviously was rookie last year. I don't know I was I'm just gonna be skeptical just because The initial one was such a steep like time frame like just a long time frame that I'm like, okay Well, I'm gonna question it every step until he's actually like You know throwing downfield full reps and everything 399 jack do Han virtuosy purple Even though to be fair in the Niners offense, you don't do that You don't throw more than like 20 or 25 yards downfield Very disappointing how that came in. It's still good news for purdy though Refractor estaban oakland for alpine a pink refractor daniel ricciardo. Dude daniel ricciardo the pink and purple's all over 75 mclaren Yeah, I think we're all just playing on that news to drop officially Refractor Fernando Alonzo Alpine Watch it's not gonna happen now like the Brady retirement Jess missed out on all the creative board of exercise. I thought they're gonna get rogers The darkness retreat made them retired and then they let mike white walk and then it's like Not one guy Chris Trevler I think he was They were so bad Magnuson checkered flag hoss Three months, I was gonna say us a little more than 60 days First stop and refractor red bull still three months. I mean, that's that's june. That's literally When you're supposed to start like ramping it up lancetrol checkered flag. Yes, then Martin Purple green the class on tf. Another printing plate here is mike crack Mike crack There we go Who is uh, what team is mike crack? I always forget Sean and sam joke about this guy all the time. It's my dad's name What team is mike crack? Is it assamarin? Yes, what looks like Yeah, okay I'll just make I'll just make sure on the checklist Assamarin. Thank you, Sloan.  I don't know I'll ask him if I meet him We're probably saying it in american accent. It sounds a lot worse and I'll maybe I'll just pronounce it A mini diamond fit the polity for seruz to 299 Maybe we're missing an accent thing somewhere Like cross or something refractor bolt us for alfa romeo Hey refractor magnus infrahass And a purple green lando norris striver of the day emilia romagna for mc laren All right, let's do that random. They'll do a recap Before I do this random. I'm getting you guys linked for bowman's best It's the best of bowman Diders fill these carnals on sale last three teams And we also have allure hockey everybody. That's right allure hockey 13 to go 10 box case number one. So 10 autos in that break art to grand prix manza Um, random to everybody here Six five and one top team gets it one two three four five and six ferrari The might crack printing plate Uh purpling green Latifi purple duhan ver stop in riccardo for sure Alonzo mini diamonds of norris vettel russell Fit the polity wolf purple checkered flag perez perez reikinen pink riccardo pink reiway riccardo goldway riccardo gold wave a sewer gold checkered ghastly gold wave auto of ralph boscham and Frederick vesti and a lewis hamilton printing plate Two printing plays for Mercedes. Congrats on this one. That's a big one. That's gonna do it everybody. The dynasty's coming up


What's going on guys got Kyle here with latent sports cards and we are riffing five boxes of 2022 tops chrome sapphire This is number 14 a random team style did a random eyes before the break We'll show you again here head brain and D with the d-backs down to Charlie C with the brewers Can always check the results of our randoms on our website guys latent sports cards calm all the way at the very bottom Got the results tab. Good luck. Good luck. Let's see what we got. Oh, yeah, Durana caught. Yeah Yeah, both those guys are in this I forgot. Yeah, costs us in Durana both solid Cost us can definitely get some hitting going. I think Durans been playing better, right Carl. Alrighty guys. Good luck Let's see some low numbers First up. We've got a Robbie Grossman. Um, that is MVP meets rookie. So this one's gonna be a random. I believe it is That's Harper and it's wander. So we'll do a random between the two teams No, I guess I can just roll a dice actually We'll go one two three on the dice goes left to wander four five six will go to Bryce Harper the Phillies It is a four gonna go to the Phillies on this one Phillies That got a Corey Kluber Javi Baez got bomb and rookie got slam Diego and you Darvish Orange that is a high five highway for the Dodgers and orange is show. Hey nice one there for the Angels That is 11 of 25 on the show. Hey orange. We'll mag this one angels. That's our D Nice hit there on the show. Hey orange Very nice Eduardo Rodriguez for the Red Sox now Jackson co Rookie got gold now got verlander and gold is Antonio Santatella that's for the Rockies on the gold number to 50 Alex Dickerson Jorge Polanco Shoes a monster man. I take any any numbered Shoes card for many product at this point Dallas Keichel's Soto. We've got the Guardians team card and a Cole Calhoun I feel like every couple days. I see a new show. Hey stat. That's like Done the first thing in a hundred years pretty much like geez man. Khloecki got John means Verdugo Jordan Lyles, and this is Josh Harrison gonna be for the A's another orange to 25 nice one there ace getting the Getting a hit in the combo spot Last pack of the first one Yeah, this is just regular Chrome Chrome sapphire There's Yandy Diaz one of the best hitters in the league Bradley Zimmer and Matt's and a O'Neal Cruz nice rookie there pirates O'Neal Cruz sapphire rookie Here's box to All right guys sold out on both the leaf pearls nice one Next thing we got to fill is select basketball H2 that is 21 22 years. So that's Kate Cunningham Evan Mowley Josh Giddy Franz Suggs a lot of great players in the 21 22 class trying to fill some select H2 That's got 15 left next one to fill got Rizzo Hoffman Iglesias and future stars Andrew Vaughn Nice one there for the red socks or white socks There's a TJ Fridle rookie and gold. This one is Louise Garcia for the Nationals there on the goal to 50 Montgomery Tyler Gilbert rookie Menden India Wu socks games recently Carl Rafael Devers Robbie Ray Charlie Blackman is a Marcelo's playing for them now, right Carl the Wu socks There's Cattel Marte Austin hedges Owings and the Rangers on the team cart Rangers got Arietta Kiermeyer Moran and Joey Vado Joey Vado Otto. Hey appreciate Jason ground a couple spots in select a Shaquilla grabbed a couple of select footballs and Jason with that last leaf appreciate you guys and Appreciate Michael grabbing a spot in the bowman chrome sapphire Always in Portland right now gotcha gotcha There's a purple Ian hat and purple is Xander Bogars for the red socks that one's numbered four of ten You go Alvin. That's a that's a forest card right there Bogart's purple to ten Another triple card here Dodgers and Brewer's Two out of three is majority, right?  Yeah, that'll be Dodgers there on these stat leaders You know my math was And run into a triple in a while there's Simeon Farmer Rosario and Louise Garcia Brian de la Cruz rookie Daza and gold this is Lordus guerrilla for the blue jays their number to 50 Lordus Got lands Thomas Alrighty guys box three It's some leaf pearl going after this one on two breaks are both full Hitting the train. That's awesome. That's awesome Carson Kelly Freeland Shane McClannahan Sion Shane and Phillies Yes, right Jeremiah. They picked up a lot of people man Kyle Lewis. They got Longoria Strasburg Keller Bradley and Mike trout. I picked up a good bit of people this offseason germana. I didn't notice that There's an Evan white. We got orange It is gonna be Brandon belt number to 25 nice color match there for the Giants Bassett Jose a braille got Max Kepler Deekman Alex Cobb and this one is braves team card there to Val Riley and albis Garrett Richards Brady singer Jackie Bradley and Louise heel rookie. There's Jack Flaherty Yon Gomes and a 50. We got Bryce Wilson for the Pirates That is 29 a 50 and we've got a drew Rasmussen. Yeah, they are Jeremiah They've been really surprising them the Rangers Trevor Rogers Wisdom Matt Chapman been a couple surprising teams this year I mean the Rays are pretty surprising as well, but they've cooled off quite a bit since uh since that starting run There's Escobar kind of Lario Lurie Garcia and a Cabrion Hayes future stars Alrighty guys two boxes left tops chrome sapphire geez so the trains get hit pretty often and I guess I Guess the timing would have to be pretty good, but that is kind of cool They got a the trains going right by the stadium if you're like you take the train every day that'd be kind of cool. Oh red That's red It is Raffi devbers on the red for the red socks. That is three of five There you go Alvin a lot of red there a lot of red red socks Raffi red socks there nice one of five. We'll make that for you Alvin. Really nice Raffi there Doing well on the the veterans Yachty Molina Chris Archer we've got the Cardinals team card there How's your guy almost here? Yeah, I got I was wondering what you're looking at. I was like somebody out there Got a goon third That is Marlon's team card and goal. This is gonna be Abyssal Garcia number 250 For the brew crew got Byron Buxton Yeah, we're hitting with those uh some veterans here for you Alvin for sure Got the devbers to ten and now or sorry the Bogarts to ten now the devbers to five There's a gold rookie. This one's gonna be Orioles rookie Alex Wells picture number 250 there for the O's Bruce Zimmerman is a Lothar Patino Ty France Carlos Correa Will Smith Collins Houser and Willie Castro Juan Soto, we've got gold. It's Xander Bogarts for the red socks Number 250 Alvin's about to get the Bogarts rainbow going got the purple the ten now the gold to 50 McCann got the Reds team card there Andrew Benintendi That is the Blue Jays team card Aaron Hicks Shane Bieber And one box left guys Appreciate Anthony grabbing the last spot in the Star Wars galaxy Neil grabbing a few tiered for crown Royale appreciate that Neil Got Hano grabbing a six series spot appreciate that and we got Chris grabbing some late in gaming She guys are just it looks like we got some late in gaming person was going right now as well And Steven G grabbing a select basketball appreciate that guys. We're filling up pretty nice here Pretty nice here guys last box of tops chrome. Good luck. We got um we pearl coming up next those two are full It's a bold prediction illegal. It's a bold prediction I'm thinking Victor win Benyama. I'm thinking these seven foot four guy that can shoot threes and play like a Play like a point guard. I'm gonna go with that guy. Let's go Donnie. We're there Kyle. He's juiced up now. Let's go He's juiced. We're doffo Castro rookie got martin Perez liftoff Astros team card and Giants team card Purple Xander Bogarts It is Michael Taylor on the purple for the Royals that one is numbered five of ten Five of ten Patrick wisdom Zach E gone number one. That's a good call Oscar Sheboy. He also won a a wooden award Jansen got Luis Arias Best hitter in the league right now man Absolutely insane what he's doing. There's a Patrick Corbin over ten rookie. We've got a team card. That's going to the Dodgers there Arias Wayne Wright and Bueller. That's two out of three going to the Dodgers and Aussie albis A couple more packs. Got a Jake Myers rookie for the Astros Urania Tigers team card and Xander on the base Yeah, I think they're saying Brandon Miller it to Jeremiah I think they're saying Brandon Miller it to over a scoot. There's a Joe Ryan rookie Alpharo Mitch Moreland and Luke Voight and last pack here guys Tops chrome sapphire and a golden it got a curving Castro Kilba do and our gold is gonna go to the Red Sox again Travis Shaw Number 250 for Alvin 33 of 50 with a Ryan Valade rookie on the back. Alrighty guys. We'll do a quick hit recap with some uh We'll go 50 and lower here about that So we had to 50 Travis Shaw Xander Bogarts Alex Wells rookie Abyssal Garcia Bryce Wilson Lordus Gurriel and Louise Garcia and Antonio San Zatella We had oranges to 25 Brandon Belts and Josh Harrison We had purples to 10 Michael Taylor and Xander number to 10 And our mags we had number to five Rafi devours nice one there red Sox on the red and Shohei on the orange number to 25 nice hit there for the Angels RD All right guys that will do it for tops chrome sapphire got leaf pearl coming up next give me just a minute We'll get that one going


Good afternoon, Jeannie Ward-Waller with the California Bicycle Coalition. Also, I'm supportive in concept of including transit funding in the special session. And thanks, Senator Hill, for his leadership. From the Bicycle Coalition's perspective, I think as we're talking about greenhouse gas reduction funds, there are other investments that can also help to increase transit, such as improving bicycle and walking access to transit. And also investing in subsidized transit passes for low income residents and students. So I think there are other investments that we also need to be looking at that can help move our transportation system for the greenhouse gas reduction fund. Thank you. Thank you. Good afternoon.


any questions so far what you have discussed? So, we have been discussing I think in the last class we talked about the limit theorems right law of large numbers and central limit theorem. Now, as we move from probability to statistics now what we will be doing is we will be trying to look mainly at the data and trying to see that from which underlying distribution or what are the parameter associated with the distribution that is likely generating this data. Whereas, the probability was about we already took some distribution and try to understand its properties and in probability like we already start with some distributions all the parameters everything is known and according to that we talk about data being generated. Now, in the statistics we do not start with distribution directly we may start with some model of the distribution, but we do not know its complete characterization we do not know what are its parameter, but we will start we will have access to the data and from that data we will try to see that what is the underlying distribution or what are the parameter of that underlying distributions. For that let us have a quick recall on all the distributions we talked so far we will expand this in this class today, but as a recap in the discrete case we talked about Bernoulli, binomial, geometric and Poisson and notice that all of them are coming with certain parameters ok. And also in the continuous case we talked about uniform exponential Gaussian Rayleigh and I think we made some remark about other distributions like a Laplace distribution and couple of other distributions. Now, if I tell that ok data is normal with mean and sigma square I may say that data is coming according to the law which is Gaussian with parameter sigma and sigma mu and sigma square. I may just say that ok data is coming from some Gaussian distribution with some parameter mu sigma square. If I specify what is the value of mu let us say if I tell mu is 0.5 or some value like sigma square is 1 then I have completely specified the distribution and here you do not you somebody do not need to give you data you can yourself generate the data as using this parameter. So, this is like if I tell this parameter this is completely specifying your probability. This is like a probability on the other hand I may say that ok data is coming from some distribution which I am going to assuming to be mu square, but mu is unknown and may be sometimes even sigma square is also unknown. What here what I am just assuming data is going to be I am instead of assuming some arbitrary distribution I am going to restricting to Gaussian distribution, but here I am I just do not know what is that parameter mu and sigma square are. Now in statistics we will try to infer this parameter mu and sigma square from data ok. So, sometime infer we call sometime we called estimate and all like we will make that more formal ok. So, to infer this parameters we need data and that is why even though we start with some underlying probability model when I talk about statistics I will always say that we will start with data and from that data we have to find out the parameter of the distributions. Ok now as I said in we want to little bit expand our family of distributions we know and see what are the parameters they are associated with ok. The first distributions we are going to look into is gamma distribution here I cannot write so, I cannot write in this I will just use the mouse. Gamma distribution is parameterized by two parameters alpha and lambda both alpha and lambda are positive and last time we discussed the definition of gamma function right. So, we all know the classic gamma function, but that gamma function can be further parameterized ok with some parameter like if you just if you ignore this denominator and let lambda equals to 1. So, that is x to the power alpha minus 1 e to the power minus x when you integrate it between 0 to certain number that will define the gamma function at that number, but now you can bring in this another parameter lambda. So, then if you add alpha to the power lambda x alpha minus 1 and e to the power minus lambda that is like a generalization of your gamma function and now if you see that if you normalize this integral by this actual integrand you will see that this actually when you integrate it over the whole range from 0 to infinity this normalizes to 1 this integrates to 1 that is what we discussed last time right. So, this is a valid probability density function. So, this is positive valued and area under this curve is 1 ok. Now, as you see I have plotted it in two scenario in the first scenario I have hold this lambda to be constant to 0.2 and then I am varying alpha. As you see that as I go from alpha equals to 1 to 2 to 3 then alpha equals to 1 this is like a monotonically decreasing then I made alpha equals to 2 it started first increasing and then decreasing and as I am increasing alpha it looks like it is started only showing increasing behavior. So, that is why when you have when you if you look into different value of alpha it is shape is changing it from monotonically decreasing to all the way monotonically increasing. So, the shape is changing that is what we call this alpha is shape parameter and here I have plotted for a fixed alpha different value of lambda when it is lambda equals to 0.1 it was like monotonically increasing, but it also showing some small tendency of decreasing when lambda equals to 0.2 this is also increasing and decreasing lambda equals to 0.3 increasing and decreasing. So, as we are increasing lambda it is taking larger and larger values in some particular peak regions right. So, basically what it is happening lambda is in kind of scaling and that is also kind of evident from this maybe not so evident, but anyway as you see like as we are increasing lambda it is kind of scaling like y values are getting more scaled not across entire range, but in some particular regions where the peak is happening ok. Because of this sometimes this is also called scale parameter. Now, even though we have discussed this gamma function, gamma distribution in terms of gamma function it has relation to some previous distribution that we know. What is that? Suppose you take some integer n and take n number of Gaussian distributions that are sorry n number of exponential distributions coming from parameter lambda with lambda and they are all IID if you add them the resulting distribution is exactly going to follow this PDF that is it is going to be gamma with parameter n and lambda ok. So, this gamma distribution can be interpreted as gamma distribution when n is integer it can be interpreted as sum of n IID exponential random variables with parameter lambda. So, basically the gamma distributions we can now take any value of n and lambda right because these are n and lambda parameters it is not necessary we have say we have never said that so far in the gamma distribution n has to be integer only as a special case we showed that when n is integer then gamma is related to the sum of IID exponential random variables. So, now let us look into what happens if I restrict myself to some specific values of alpha and lambda. So, here I have taken alpha equals to half and lambda equals to half. So, here the first parameter not integer I cannot interpret it as a sum of half exponential random variable with parameter half I cannot interpret. But this distribution gamma half and half this has a special name and special significance this is called chi square distribution with 1 degrees of freedom and it is denoted as this symbol chi with subscript 1, 1 is denoting here 1 degrees of freedom and chi squared the 2 is the superscript 2 is denoting chi squared ok. In the gamma distribution if you are going to set alpha equals to 1 and lambda equals to half this is the distribution you will end up that is simplified one for the specific value of alpha and now you may be wondering ok fine you have taken alpha equals to half then where is this 1 degrees of freedom why that term is coming ok. And just to see that why could that why this has been given the name of 1 degrees of freedom. So, suppose let us take uniform distribution sorry let us say u is some random variable which is normal distributed. Now you can show that if you take the square of that that has this gamma distribution that is square of a normal distribution is chi square distribution with 1 degrees of freedom ok. You see that now u is I have just taken u to be 1 random variable it can take any value as per that probability density and if I just square it I am getting gamma distribution and here u is one component which can take any value it likes as per that ok. And if I am just squaring that I am getting this gamma distribution ok ok next there is another if you now this instead of a gamma half and half if you take gamma n by 2 and half ok. Now this is also given a special name this is just like extension of this chi square distribution with n degrees of freedom and here n is like an integer and that is denoted as chi square with a subscript of n. So, then what is chi square distribution with n degrees of freedom this is nothing, but a gamma distribution with parameter n by 2 and half and if I plug in the value n by 2 and half in this pdf we will we will get back this value. Now again this chi square distribution with n degrees of freedom this is again related to other distributions. So, let us say if you have n random variables n iid random variables I am now considering two cases case one where all of the random variables have normal distribution if you square them and add that will have chi square distribution with n degrees of freedom. So, when n equals to 1 when this n equals to 1 we had already this case that we have got. So, it is not just that only Gaussian is related to this gamma distributions you can even verify that if all this u is are exponentially distributed with parameter half and if you are going to add them and all of them are iid then also you will get gamma distribution with parameter n comma half notice that here it is not n by 2 it is n here and now even though I have stated them here you should check this check this this is indeed correct ok. Make sure that if you are going to add all this if you generate n iid random variables which are normal and if you are going to add them you will indeed get this chi square distributions ok. Now let me say I think at some point we should actually start simulating this and say.


Hello, welcome to the Koenig section YouTube live session today So those who have just joined in Please type in your name in the chat box so that I know who all are attending this session All right guys, so today's session we are going to start with the fact that why at all Koenig sections Are known by the name Koenig sections, okay? so Koenig section is basically Given the name because they have been obtained by the section of a right circular double cone with a plane Right, so these Koenig sections they are obtained by They are obtained by the cross section of a right circular double cone a Right circular double cone by a plane Okay, so depending upon how these planes or how this plane passes through the right circular double cone Different Koenig sections are generated. Now. What is the right circular double cone a cone which has got? Let me explain this to you first a cone is basically Right the right circular double cone is basically a structure like this where this is called the axis of the cone So this line is called the axis of the cone, okay, and these two lines are known as the generators These two lines are known as the generators When the axis of the cone makes 90 degree with the base of the each cone We call it as a right circular double cone. Okay, so I will now show you How basically these Koenig sections are generated? Okay, so let us focus on Let's focus on this structure So I can as you can see on your screen. Okay, so basically this is nothing but a right circular double cone Okay, so I've shown it in a 3d structure now this right circular double cone if I cut it by a plane which is perpendicular to the axis Right as you can see here I've cut it by a plane which is perpendicular to the axis the cross section area from the top you can see is that of a circle Okay, so the cross section area that you can see is that of a circle Okay, if you cut it by such a cone Or such a plane which is making some angle Okay Then you realize that you start getting different types of Koenig's Okay In this case you end up getting a hyperbola Right, so these basics are all cleared in your mind And if there is any question regarding the basic of creating a Koenig section, please do ask In fact, I will quickly brush you through So when you cut this by a plane When you cut this by a plane Whose angle with the axis let's say is Let's say I call the semi vertical angle of this right circular cone as as alpha And let's say this angle is theta Okay, the angle of between the plane And the axis is theta if theta is 90 degree it generates a circle Okay, and If this plane passes through the meeting point of these right circular double cone the circle would be a point circle Okay If this theta is somewhere between 0 to somewhere between Alpha to 90 degree Alpha to 90 degree it will create an ellipse It will generate an ellipse Again here. I'm assuming that it is not passing through the meeting point of the generators Okay If theta is exactly equal to alpha That means the angle made by the plane is parallel to either of these generators The cross-sectional area left would be that of a parabola. Okay And if theta lies between 0 to alpha Then it would end up cutting both the Naps these are called naps Okay, both the naps Of this right circular double cone And you will obtain a hyperbola in that case If it passes through the meeting point if it passes through p if the conic section passes through Or if the plane passes through p if the plane happens to Pass through the point p Then in that case we call the conic generated as a degenerate conic Okay, and pair of straight lines is an example of a degenerate conic So first I will spend some time on the degenerate conic In order to explain you What is the general form of the equation of a conic section? So let's talk about pair of straight lines briefly What's a pair of straight lines? Pair of straight lines is basically a kind of a degenerate cone Where you obtain the Equation of this pair of straight line by multiplying two lines Okay, so if you start by multiplying two such lines which are passing through Let's say origin y equal to m1x and y equal to m2x Okay, if I ask you these are the lines which make that pair of straight lines Then the combined equation of the pair of straight lines would be y minus m1x times y minus m2x equal to zero Right, so this is the equation of a pair of straight lines, which is passing through origin Which is passing through Or intersecting each other at origin So both the straight lines are passing through the same point origin, okay If you clearly look at this expression It's very important for you to appreciate that This expression will be a homogeneous Expression in x and y Okay So we call this as a homogeneous function or homogeneous equation in two variables This is going to be a homogeneous equation in two variables Of degree two Of degree two So what is A homogeneous equation a homogeneous equation is basically a equation where you would realize all the variables are having the same degree For example x square y square x y they are all having the same degree, okay So any second degree equation, which is homogeneous in nature in two variables That would always represent a pair of straight lines passing through origin. This is very very important so always remember this Any equation of this nature a x square plus two h x y plus b y square Will always represent a pair of straight lines Passing through origin Now it is not necessary that both the lines would be real in nature It may happen that you may also end up getting non real lines as well, right You may end up getting imaginary lines as well that depends upon some relationship between h a and b that I will discuss with you later on Okay, now taking a clue from this You would realize that any conic that you see is going to be having a general formula or the general equation as a x square plus two h x y plus b y square Plus two g x Plus two f y plus c equal to zero Right, this is the general structure of any conic section that you would come across Right, which is called a second degree general equation of a conic section So even your straight lines as you can see here The the homogeneous its equation itself is basically is a second degree equation Even circle parabola ellipse will have these six terms appearing not or it's not necessary that all of them will appear together It may happen that some of them may be absent Now how why is this a second degree equation? Guys, if you if you see a very specific case from the example which I cited a little while ago the equation of the equation of if you see the equation of a cone I've taken passing through the origin as z square equal to x square plus y square, right? So this is the equation of the cone Okay And if you take any line any plane, okay, let's say I take this plane x plus y plus z equal to one Okay, and you try to eliminate your z from these two equations So from the plane equation and the cone equation if you try to eliminate your z Okay, you would realize that Let's say this was the equation of the cone Okay And let's say this is the equation of the plane any plane. Okay, so I'm taking just a simple example of a cone and a plane If you try to eliminate your z that means replace your z with one minus x minus y in this You yourself would see that When you square such terms You will end up getting some terms in x square Some terms in y square You'll see some term with x y You'll see some term in x you'll see some term in y and you'll see a constant, isn't it? So that is what we are trying to state in the previous slide that any conic section would have This kind of a structure. Sorry. This kind of a structure a x square Plus 2 h x y plus by square plus 2 g x plus 2 f y plus c equal to 0 Right so far any questions with respect to this Okay, so this is the general structure of any conic section Now depending upon your values of a b and a b h g f and c This conic section can represent various things Right, so now we'll discuss the condition to represent various conics condition to represent various conics The first condition that i'm going to talk about that's the very important condition if a x square plus By square plus 2 h x y plus 2 g x plus 2 f y plus c equal to 0 has to represent A pair of straight lines If it has to represent a pair of straight lines then An expression delta which is given as a b c plus 2 f g h Minus a f square Minus b g square Minus c s square will be equal to 0 that is In a simpler form the determinant made by these terms Will be equal to 0 Right now first of all i will prove how these condition comes So let us prove how this condition comes Okay So let us start with the fact that let A x square Plus by square plus 2 h x y Plus 2 g x plus 2 f y plus c equal to 0 represent a pair of straight lines Okay, let's say this represent A pair of straight lines Of course since this is not a homogeneous equation That means Their point of intersection of these lines is not origin because had it been origin These three terms would have been absent Right So let's say these pair of straight lines This pair of straight lines intersect each other at Let's say they intersect each other at x 1 y 1 And we are assuming that these lines are also not parallel to each other Okay Then do one thing then apply the concept of shifting of origin Shifting of origin 2 x 1 y 1 That means i'm assuming the point of intersection now to be my new origin Okay So when we do that all of you remember the concept of Shifting of origin where you replace your x with Where you replace your x with capital x plus x 1 and y with capital y plus y 1 So this was the concept which we had discussed In the beginning of the coordinate geometry chapter in class 11 So when you do these replacements in your equation Given to you you get something like this a x plus x 1 square Okay, b y plus y 1 square Plus 2 h x plus x 1 y plus y 1 2 g x plus x 1 2 f y plus y 1 Plus c equal to 0 Okay And if you simplify this you are going to see something like this a x square b y square 2 h x y And apart from that you will see terms like x 1 I'm collecting terms having capital x in it so 2 a x 1 I will see then from here I will get 2 h y 1 and I will also get term like 2 g Similarly if I collect terms containing capital y I will get 2 b y 1 I will get 2 h x 1 And I will get 2 f term correct And if I collect the constant terms I will get a x 1 square b y 1 square 2 h x 1 y 1 2 g x 1 2 f y 1 plus c equal to 0 Okay Now all of you please listen to this very very carefully If you want this pair of straight lines To pass through origin It is passing through origin Then it is very clear that it has to be a homogeneous equation And if it has to be a homogeneous equation That means this term This term And this term should be 0 Remember I discussed with you Any homogeneous equation Of second degree is basically representing a pair of straight line passing through origin And since I am shifting my origin to the point of intersection x 1 y 1 It means that I am assuming that These terms are going to be 0 This term is going to be 0 This term is going to be 0 And this term is going to be 0 Is that clear? Because if these three become 0 I will only end up getting this term Which is a second degree term And hence it will represent a pair of straight lines passing through origin So this implies we have a x 1 H y 1 plus g equal to 0 We have this is x 1 Yeah, this is h x 1 Plus b y 1 plus f equal to 0 And guys if you note your expression very very carefully If you note these expressions very very carefully you would realize that You can write this as x 1 into A x 1 Plus h y 1 plus g Plus This expression I am simplifying Plus y 1 into h x 1 Plus b y 1 plus f And the remaining terms would be g x 1 f y 1 plus c So what I did is I took an x common from this term And one of these terms I split it open as H x 1 y 1 plus h x 1 y 1 So I took a x 1 common from this term and I took x 1 common from One of these terms So this also I split it up as g x 1 plus g x 1 This also I split up as f y 1 plus f y 1 So one of the terms a x 1 h y 1 and g has come from taking this term This term and this term Similarly for y 1 if I take y 1 common from this term This term and this term I get this term I will get this term, okay, and the remaining terms that is G x 1 f y 1 and c I am writing it over here Okay, is that clear any question regarding this so far Now from 1 and 2 we already know that These two are 0 this is 0 This is 0 Correct that means I get a third equation from here That is g x 1 f y 1 plus c also equal to 0 So I get three equations altogether Like this So this is my third equation Now using these three equations I would now eliminate x 1 y 1 Okay, so from this you try to eliminate x 1 y 1 Okay, and how do I eliminate it if you remember The trivial solution concept of A system of homogeneous equation or a system of linear homogeneous equation The determinant If this determinant is equal to 0 Okay, then this system of equation.  They are not going to be be a trivial solution over here Okay, so if if the system of equation doesn't have any trivial solution We can say that the determinant formed by the coefficients Okay, so basically let me treat one over here if nothing is there So the coefficient of these variables would form a determinant which is equal to 0 right And if you expand this you are going to end up getting the desired result which is abc plus 2 f gh minus af square Minus bg square minus ca square equal to 0. Is that fine? Is that clear? So this is the condition Which we write in a very short form as delta Okay, so if delta is 0 your second degree equation will definitely represent a pair of straight lines Okay