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Frequentist makes it possible to forecast the probability of a future event based on the current frequency. Frequentist works because of the law of large numbers. There are two different versions of the law of large numbers: the weak law of large numbers and the strong law of large numbers. In 1713, Swiss mathematician Jakob Bernoulli after 20 years of hard work proved that (if you have a sample of independent and identically distributed random variables, as the sample size grows larger, the sample mean will tend toward the population mean.) the sample average converges in probability towards the expected value This known as the Weak Law of Large Numbers or Bernoulli's theorem. It tells us as more trails performed the frequency will more likely to become closer to the true probability. Be aware that it is only more likely not a 100% guarantee. Bernoulli’s theorem gives us confidence that a random event has a great chance to have a certain probability. In 1930 Andrey Kolmogorov pro...

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Almost all statistics we carry on today are based on frequentist probability.  Frequentists believes as the number of trails increases the relative frequency will get closer to the probability of that event. For any given event, only one of two possibilities may hold: it occurs or it does not. if a random event is repeated many times the frequency of it will be its probability. For example, to get the defective percentage we collect enough samples and use the defective products to divide all products. Frequentists believe there is a certain probability of every event. As long as we do enough trails the frequency of that event is approaching the probability of it. The idea of repeat the random many time and using the frequency of it to review its probability is easy to understand. However, maybe you have the doubt that frequency and probability are two totally different concepts how can you confidently apply this theory to measure all random events? To answer this question let me do...

Probability is another pillar that supports the statistics temple. It is the tool we use to measure and quantify randomness. There are three common definitions of probability. These are the Axiomatic definition introduced by Kolmogorov (1933), the relative frequency definition described by von Mises (1915), and the classical definition for equally likely outcomes. Here they are. Now please allow me to explain them one by one. Just kidding. Don’t close the video. When learning a mathematical concept, the alien’s feeling of the math language can easily be overwhelming. Also, lots of concepts that are not particularly interesting and you probably have no idea where and when you will use it. So as you know the lack of motivation means that most of them are quickly forgotten.  Math exis to address the real-world problem, it doesn’t have to be that abstract. Here let me try to explain it in plain language: Probability is the branch of mathematics concerning numerical descriptions of h...

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We finally come to the last foundation of statistics and probability. Quantify probability. If I said, my favorite team more likely to win the next game you probably feel that is a vague  statement. I can do it better: my favorite team has an 80% chance to win the next game. How to come to that percentage? Well, you may think it must be very complex and even unachievable. Actually, there are only three principles when quantifying the probability. Permutation and combination method: let us see an example. What is the probability of a rolling dice stop showing 6? There are 6 positions the dice may end up: 1 2 3 4 5 6. 6 is one of them. So that the chance of getting 6 is 1to 6. The key to quantifying probability using the permutation and combination method is finding all possible outcomes. we can use permutation and combination to deal with a single random event but what if there are multi random events? Sum method: when calculating the chance of a happens or b happens we can sum each...

Once upon a time, me and my wife want to decide who will wash the dishes after lunch. She proposed that we should toss a coin. But you already win 5 times in a row. That coin seems on your side. I said. “You have a 50% chance to win, you already lost 5 times so today you are more likely to win!” Really?? To answer it please let me introduce the second piler of statistics and probability - Independent variable. A variable can be an object, event, idea, feeling, time period, or any other type of category you are trying to measure. Therefore an independent variable is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, whether tomorrow is raining or not has nothing to do with what you eat tonight. So whether tomorrow is raining and what you eat tonight are independent variables. Raining or not tomorrow has nothing to do with what eat tonight.   On the other hand, the dependent variable is something that depends on other factors...

Randomness is one of the most important pillars to support the statistic and probability temple.  Randomness is unpredictable. In the common parlance, randomness is the apparent lack of pattern or predictability in events. Please remember: Randomness is unpredictable but it not equal to uncertainty. Let’s say team A has a 60 percent chance to win the game, that percentage is a certain number although you can’t tell whether they will win or lose next time. We can consider randomness is that we know all the possibilities, the only thing we don’t know is which one will happen next. Flipping a coin, you don’t know whether it will show head or tail, but it must be one of them. Shuffle play music, although you can’t predict which song will play next, it must be one on your playlist.  On the other hand, uncertainty is we have no idea what can happen next. For example the Black swan theory - something that comes as a total surprise. Bay the way all swans in New Zealand are black, he...