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One of the more important ideas in probability and statistics is known as hypothesis testing, and one of the central ideas of hypothesis testing is known as the null and alternate hypotheses. These are based around the two fundamental problems of probability and statistics. In probability, the problem is this. Given the true state of the world, predict the outcome of a random experiment. So for example, if you know that, in fact, a coin will land heads with probability one half, what will happen if you toss a coin ten times? On the other hand, in statistics, we have the fundamental problem given the outcome of a random experiment infer the true state of the world. So suppose we see a coin land heads six times out of ten. What is the probability the coin lands heads? Now generally speaking, answering a question like what is the probability of something is a little too hard for us to answer. And to make it easier to answer these statistical questions, we consider two hypotheses. The first is known as the null hypothesis, sometimes indicated H0, and the other is called the alternate hypothesis, indicated HA. And you can think of, as the ultimate goal of statistics, the question, which of these two hypotheses do I choose to believe? More formally, we can state the problem this way. How likely is the observed outcome if the null hypothesis is the true state of the world? As an introductory example, suppose we have a bag which either consists of all black jelly beans, or a mixture of black and green jelly beans. Now we don't know which bag we have, so to decide we'll pick out a handful of jelly beans and find that it contains a mixture of black and green jelly beans. What do you conclude? Well, any normal person would say that we have the bag of green and black jelly beans, but statisticians are not normal people. So let's think about this statistically. The null hypothesis is that the bag consists of all black jelly beans. We'll discuss why this is the null hypothesis later, but for right now we'll just take this as the null hypothesis. The observed outcome is a handful of black and green jelly beans. And remember the problem that we want to answer is how likely is the observed outcome if the null hypothesis is the true state of the world? And so we can ask the question, how likely is it that we get a mixture of black and green jelly beans from a bag consisting of all black jelly beans? And that probability is zero. It is an event that cannot happen. And so we reject the null hypothesis. What's important to understand here is the logic. You do not get to choose your facts. The observed outcomes are what they are. So you have a choice between two hypotheses. One hypothesis requires a fantastic stroke of luck in order to produce the observed event. In order to reconcile your belief with your observations, you either have to reject all of the evidence or you can change your mind.   So let's go back to that first question. Why did we choose bag consisting of all black jelly beans as the null hypothesis? And here it's useful to keep in mind the following idea. You might be a null hypothesis if you could make a specific quantitative prediction and you could be falsified by an observation. For example, let's consider our two possibilities.   Now the hypothesis all jelly beans in the bag are black allows for a specific prediction. Every jelly bean we pick will be black. In contrast, our other hypothesis doesn't allow us to make a specific prediction. The best we can say is some are going to be black and some are going to be green and that's not very specific. The second important observation is that this hypothesis all jelly beans in the bag are black can be falsified. If we pick out a jelly bean and it's not black, we know this is false. In contrast, this second hypothesis, some jelly beans are black and some are green, no observation can falsify. And the next jelly bean we pick could be green. So for example, if you're trying to decide whether a coin is fair or not, so you flip the coin 100 times and record the result. Identify the null and alternate hypotheses. Well the two hypotheses are the coin is fair or the coin is unfair. And so the first question is, will one of these allow us to make a specific quantitative prediction? And this first hypothesis will. This allows us to make a quantifiable prediction. The coin will land heads about 50 times. Human psychology being what it is, sometimes it's easier to see when something doesn't work. This second hypothesis does not allow us to make a quantifiable prediction. The coin will land heads, I don't know how many times. And so what that says is that the coin is fair is going to be our null hypothesis. Now an important idea for what's known as Bayesian statistics is the following. You're trying to decide whether a coin is fair or weighted so it lands heads 40% of the time. To do so, you'll flip the coin 10 times and record the number of heads. Identify the null hypothesis. And again we have two possibilities. The coin is fair or the coin is weighted to land heads 40% of the time. Our first hypothesis leads to a quantifiable prediction. The coin will land heads 5 times in 10 flips. What's important about this example is that the other hypothesis also leads to a quantifiable prediction. If the coin is weighted to land heads 40% of the time then the coin will land heads 4 times in 10 flips. Both of these hypotheses lead to quantifiable predictions which means either could be the null hypothesis. Now you might wonder why do we call this the null hypothesis? Why don't we just call it the hypothesis that gives us a quantifiable prediction? And this example suggests why that terminology is used. Suppose you're trying to decide whether a treatment increases the growth rate of plants. On that end you grow 5 plants without treatment and 5 plants with treatment. At the end of the experimental period you measure the heights of the plants and let's identify the null and alternate hypotheses. So there are two hypotheses. First the treatment did not affect the growth rate. And second the treatment did affect the growth rate. This first hypothesis produces a quantifiable prediction. The height of the plants will be the same in both groups. The second hypothesis, not so much. The treatment did affect the growth rate does not produce a quantifiable prediction. The best we can say is the height of the plants will be different. So in this case notice that the null hypothesis says there is no difference between the two samples. And in general in many cases the null hypothesis corresponds to no difference between the two samples.


So if you were to score a touchdown in the game today, won't your celebration in the end zone be? Oh. Oh. You got to hit it with us. We got to hit it? Do something like this, baby. I don't know. One for the gritty. You're going to hit a gritty? Let me see you mess gritty. I can't even do it. I'm probably doing the gritty. Can I see you mess gritty? Yeah. I would streak. That's probably true.


Here's a water wave. It's described by a wave function that determines its operation and a wave equation that determines the change in the function over time. We can channel this wave into two directions, say A and B. With enough time, we can create a great distance between the two branches. If we examine branch A at some time t and find that the wave is at a peak, we will know immediately that at that exact time the branch B wave will also be at a peak. We don't ask how did the A branch inform the B branch that it needed to be at a peak. We did not analyze whether information was flowing from A to B faster than the speed of light. We simply note that both branches are a part of a single wave equation that determines its state at any time t. Of course, if we drop channel A's water off a cliff, the wave in channel B will continue on its merry way. To help isolate the key differences between classical mechanics and quantum mechanics, let's look at one more classical example. Here we start with two coins, each with the heads on one side and the tails on the other. If we put them both into a spin and send them up the two channels, we note that during the journey they exhibit neither heads nor tails. But they carry a probability that, once stopped, they will either come up heads or tails. The probability is 50-50. But unlike the water wave, the results for one of them does not tell us anything about the results of the other. They are independent. But like water waves, the outcomes can be predicted if the starting conditions and channel environment are known. For the quantum mechanics view, we'll start out with two electrons that have been put together to entangle them. Entangled particles are particles that have their quantum states described by a single wave function. The quantum state in question here is the electron's spin. In their lowest energy state, when one is up, the other will be down. Now we send one of the electrons down channel A and the other down channel B. As they travel, they will not exhibit any spin much like the coins did not exhibit heads or tails. In this example, the moment the electron and channel A interacts with a strong magnetic field, it will bring either up spin or down spin to the interaction. At the same instant, the other electron's spin is determined. If A was up, B will be down. If A was down, B will be up. This is as expected because both particles are following the one wave function. It does not matter how far apart the two particles are.


Hello and let's talk about the number 36. Yes, 36 runs which was India's score in the second mix in the Adelaide test and which has sent shockwaves to the Indian cricket fan community. Forget words, not even memes might be enough to adequately represent the kind of feeling that Indian fans and for that matter, cricket fans across the world felt as the famed Indian batting lineup crumbled before Australia. So it's important to take this score in perspective of course. India was in fact performing decently in the first part of the test but then this collapse actually cast a grave question mark on the performance of the Indian batting order, the nature of the Indian team itself, issues of selection, issues of temperament, issues of technique. All these now are very big questions that the Indian team, the Indian management and the BCCI cannot ignore. And to talk more about this, we have Leslie Xavier, NewsClicks Post journalist and Leslie talks not only about the past, previous incidents of such sort, what happened after that, but also the very attitude, the kind of hype around the Indian team and what it conceals and what it reveals. Here's what you have to say. Thank you Leslie for joining us. So cricket fans across India, in fact, in many parts of the world are in a state of shock even now. And it seems unreal something that is from, you know, it's the stuff of stories from decades ago or whatever where India was a very weak team, did not have the resources, was a minor player in world cricket at that time. You could have thought of something like this, but at this point, it just seems unbelievable. So quick thoughts on the situation right now. So yeah, 36 is it. I mean, yeah, by any stretch of the imagination, it's, it's, it's bad. And so previous, if you look at the top five lowest scores, the previous one was in 1974, 42 against England, disaster store. And then there is one in between in the top five, you get it in the 90s. Otherwise, everything belongs to the era where Indian cricket team was nowhere in the top, even politically or in the game. I say politically because Indians are the India is the top dog in on both, both counts right now. So earlier, yeah, these scores used to be common when our team, I'm talking about pre-independence and immediately post-independence teams used to tour England or West Indies or Australia. And now it's surprising because see the kind of cricketers that we have. And India in the last three decades, four decades, I mean, also post the World Cup victory in 1983, we have slowly established ourselves as one of the strongest batting nations in the world. And so we have had very poor bowling performances where batsmen have ripped us apart in this, I mean, even even in this current decade, first part of the current decade, but batting is what not raises the red flag when batting collapse happens because India is, I mean, we have, our stars are always batsmen if you look at it. And this team also has a decent lineup of batsmen who have established their credentials in all formats. You have a very specialized test batsmen in Chatejwar Pujara, great batsmen, I mean, no doubt, but he failed in the second innings as well in Adelaide. And in fact, all the batsmen, they didn't cross into double digits, right? So that way the previous bat score of 42 previous accords, that way, at least one player had crossed. I think he scored Eknath Salkar, it was he scored 18, I think, but in this team, nobody did. I have to decipher this thing, whether the extras happen to be the top scorer. So anyways, jokes apart, looking at the team composition, of course, this team has very good ballers, fast ballers, decent batsmen, I mean, decent best batsmen in the world, credential wise, they shouldn't fail. And it, it so happened that the Australian fast ballers will prove them in that, in that critical, that, that, that part of the portion of the game, it just happened. It was a Blitzkrieg kind of a situation. And Australia themselves did not play well in the test match until that moment. So Australian batsmen had struggled in the first week. In fact, they conceded first winning lead as well, right? So it was, it was supposed to be an evenly poised match till this happened. So it's, it's very clear why it happened though, because in all the reactions where people have gotten into a pinpointing false in Virat Kohli and his aggressiveness, his brashness, among other things, it takes away what a very important aspect, which is, which is not being discussed. This India, Indians are a minnow, as far as ping ball test is concerned. They've just only played one ping ball test, day and night test before this day and night test is new in the game in any case. So it started in 2015. And the, the unbeaten team in this is Australia. They have won all the matches they have played, I believe eight. And they got into the bandwagon right, bandwagon right at the start, because they believed in it potential. They thought that Australian grounds are huge tests following is there, but still they were dwindling crowd, et cetera. The cricket Australia was worried about how to bring the crowd back to test matches. And they thought that day and night cricket, whether they are right or right or wrong, it's a matter of debate again. Let's, let's see how the game progresses in the next 10 years or so. But they got into the bandwagon and they have ensured that each home series or even ever series at least one matches there, which is day and night test. And so that experience of seven, eight matches that, that all, that is very big. While India was always reluctant to get into it, except I would say, again, last year, when Bangladesh against Bangladesh, when they played, I would say that was a gimmick itself because when Sorag Angli became the BCCI president, he had to make some, some kind of flashy move. And this was a flashy move. Like we are getting into day and night test. So it was organized in Calcutta. It's hometown, Ganguly's hometown. And against Bangladesh, see, again, Bangladesh is also new to ping ball test. And so, and it, I mean, technically a weaker side as well, and they're playing away to India. So India won that match, but that doesn't make them, make them experts in ping ball cricket. And ping ball behaves distinctly, especially certain phases of the match, when it moves prodigiously, certain phases of the, of the match, especially when in that twilight area, when the sun is fading and the lights come on, it behaves as though they are playing in overcast condition as though they are playing in England. So that I mean, so you are talking about our batsmen who are used to flat deck pitches, playing on the ice there, anyways, get, get in trouble with the slightest of movement. And then you are not used to playing ping ball cricket. And then you go to Australia and you play some of the best fast ballers, swing ballers in the world. And this is what happens. So underprepared, they went into went into the match, clearly underprepared. And at the same time, the batsmen when collapse was happening, rather than showing it up, I don't know, I mean, maybe they, they're just maybe they're not equipped well enough to play test match anymore, because the focus so much of focus on the shorter format, it's, it's, it's very difficult to refocus and understand the dynamic of a longer form game. And that to a dynamic of a game, which is alien in itself, because it's a day and night test match. Absolutely. So Leslie, when I saw the school line, I was reminded of the infamous Brazil, Germany match, actually, where Brazil let in seven goals. And even at that time, it was another example of a team which was hyped so much, there was a lot of talk about it. It was touted as one of the best in the world. And then this defeat happened, a lot of the structural issues came out. And you also explained some of the structural issues that, you know, the glamour and glitz around the Indian team basically have actually concealed some of these, some of these issues. And simultaneously, there's also the question of by now, so much of discussion about the team has become about the attitude about, you know, the hype around the team, rather than actually the technical aspects or say the performance, the technical performance of the team itself. So that's actually the interesting point as well. Yeah, it is because the main narrative of TV, if you look at it, it's, it's, it's this, we actually use this, this, yeah. So the IPA alpha, 0 main, but see, it works. I mean, I'm sure on the sporting field, it works. But on a cricket, that's not the only thing that works. That's what that's what we are missing here. So on a cricket field, and I mean, across all the formats, but especially on the test, the many layers that that sport requires you to, as a player is needed fully in the sort of formats, maybe aggression, because it's such a short format that maybe aggression and a bit of flash and all these things work. And then you get away with it. But on the longer format, it brings out your personality even that's that's how that's how they talk about test cricket. So you need temperament, you need technique, you need the right strategy, right approach in each session. So I earlier mentioned how the ping pong behave differently in certain times of the day that requires a different set mindset when you are batting there. So you might have been a set batsman till five o'clock in the evening, suddenly the land lights come out. And then it's the next session, and you have to start afresh, you have to approach the game differently. So all these things matter.   It doesn't work like that. So that's one introspection from I mean, see, these things, I mean, similar results, results have happened, similar losses have happened. Like the last test series, India played abroad was against New Zealand, you they lost there. They have lost, they've had bad losses in England prior to that in 2018. And in between earlier, you mentioned the glossing over part of it. It's not just a glamour that is being used, but it's also the record that's been used to gloss over things and record of being playing at home, which is like I said earlier, plastic pitches, you have your own crowd support happening around and weather conditions suit you. A lot of factors are there that plays place for you.  So I'm sure I mean, of course, in the dressing room, what happened, we are not we can never be very sure, but inside the dressing room, there are been there would have been an aggressive tense atmosphere when the wicket started falling. And when a new batsman is going to go in, that doesn't help. So this I this I've been always critical about Virat Kohli's captaincy is on the playing field when things are going and when wickets are falling, or you are on the field or when you're batting well, it works fine. But when when things are not happening, team needs a impassive captain who doesn't betrays emotions who emotions who doesn't shout who doesn't group. I mean, Virat Kohli is very expressive that way. And that always never I mean, that doesn't work at all. And it has been proven and of all things in the IPL because he has a great team. If you look at the players in oil challenges, Bangalore, but they're always under perform. Wonder why. So that's a question that team India management and the BCC I should ask now with this loss because when we look at the previous worst score, the 42 in 1974, Ajit Vadekar was the skipper. He came back. He lost his position even in the West zone team. He never played for India after that. And now, now, he became the captain after they took over the captain. So whatever the internal dynamic was there, but action was taken. So whether such kind of a postmortem and strict action will be taken. I mean, that's that's up to BCC is already there have been some calls happening that Rahul Ravi, who has been working with the under 19 players quite a bit now. And he has proven his coaching credentials, credentials also decently and some of the youngsters in this current team have been coached by them. So there have been calls. I think the towel driver should be there in Australia at this point, since Virat Kohli is tabling back for paternity leave. And then maybe that might lead into at some later stage, a change of era, as far as coach is concerned, maybe David taking over, but maybe because with BCC and with Kohli and maybe just having a dynamic, a stage dynamic that too, it's uncertain. Absolutely. And just to sort of the BCC, of course, having its own dynamics as well, like you said, which makes their question of whether they're going to intervene even more dicey, because I don't think I mean, I wonder if the BCC has ever been full full of drama as it is right now, it's become and say, well, like you mentioned, the previous instance when one, I just wanted to say I was involved at that time, I think the BCC was a far more unobtrusive organization, despite what we did. Whereas now in its own right, it's a media star or a sensation, so to speak. The 74, the cases, I mean, it's not very clear cut that way that the board was very, very clear as far as clarity of action is concerned. There was a lot of politics within the team. And so people were waiting for you to fail so that others can take over. If you look at the history of Indian Brigade, I mean, that era, it was, it was, I mean, almost all the eras, you had problems between Gavaskar and couple of days, couple of days and so it's always been there. So that way, I per alpha male leading the team and no questions asked. So that that way, at least it's there is a semblance of control and this kind of a system started probably with the current BCC president being at the helm as captain of India, because he was such an unquestioned leader on in a team where you add such in Tendulkar you add various other stars, David Sevag, like a previous lecture. So you were all sick. So it was a team full of stars compared to even now that way. But with with such a system, the problem is that there's no second line of command. Now we're actually is leaving people are panicking. They're saying you drive it. I mean, I'm with this loss. Send rabbit back. Send rabbit to Australia to help these guys things like that have been discussed. Rohit Sharma is a is a decent captain, but he's not a test player is I mean, he's recently joined the test court, but he has not considered a test player assets, but and also his leadership credentials have been proven in the IPL and in limited hours, we get so you can never be sure. So so BCC has to act if they have to act in in multiple ways, possibly to look at the future of what would be the leader after Koli or if at all, Koli remains, he gains his captaincy now, which is, which of a way is fine. But Koli can't be captain forever, right? Also, right? And then with this kind of leadership that has been it's like certain political practice, like Congress even. So there's no second line of leaders to in take over the mantle and take the fight to the BJP as far as electoral politics in the concern and concern. Yeah, New India is being reflected in cricket, if Koli is perhaps right. So BCC is action also they I mean, I don't know whether their priority whether they have their eyes in Australia at the moment, because within the BCC politics, there is there is a critical juncture happening because Jay Shah, the secretary and BCC president Ganguly, they have they are very keen to stay on and their mandate and tenure was supposed to end in July, pandemic situation. So things lingered on. But now they have approached the Supreme Court. And I have requested the court to take a decision on revoking certain clauses in the in the Constitution, which which was put in place after the law the panel reforms. So the main point being the cooling off period that officials are supposed to go through after continuing as in a in a position for six years, not in a position in many positions. Basically, if you have added anywhere in the state association, and then the BCC, I want to continue six year period, then you have to get yourself off any power and then after three years, come back again. So Ganguly was the head of CAV, the Association of Bengal, and Jay Shah was head of the Gujarat State Association. So both of them are supposed to go into a cooling off period, but they don't want to. And they are trying to get this done. So Ganguly is busy doing that. So whether he will be interested in the Indian cricket team, whether he'll be whether BCC is turning would affect the restart of the domestic calendar, which is not happened since since lockdown. And so uncertain, more than 5000, 6000 cricketers across various levels, women, men, boys, age group cricketers, everyone is facing an uncertain time because there's no sign that the domestic cricket is starting. So on one side, it's the national team and the international cricket you are talking about and how BCC I should intervene now to understand where the team is heading. And on the other hand, they have a larger responsibility of ensuring that the cricket from the grassroots level to Renji level, these starts and that supply chain of players that at least was in place despite all the churnings and voltage that happened in the BCCA. That's also pretty as of now. And so action, yeah, let's wait and see in the coming days after the tour because the BCCI and it makes sense as well that there shouldn't be a knee jerk action now at the tour end and then the team come back and they should be a post-mortem. But beyond that, if at all solid action would be taken, that's that remains to be seen. Absolutely. Thank you so much, Nessie, for speaking to us. That's all we have time for today. We'll be back tomorrow with more news from India and the world. Until then, keep watching.