Central Limit Theorem | Basis of the probability distribution | Statistics and Probability EP15

Central Limit Theorem | Basis of the probability distribution | Statistics and Probability EP15

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Statistics and probability

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Imagine you have an apple orchard farm, before harvest you want to know the taste of these apples.  But how? Take a bite of each one of them? Absolutely not. I guess you would randomly pick several apples and judge the overall sweetness based on the taste of those.  Wait a minute, why these apples can represent the whole orchard? Because you are using the statistics method. Actually, we just go through a famous statistical investigation (problem-solving) cycle: Problem, Plan, Data, Analysis, Conclusions, and Communication (PPDAC). According to Wikipedia: Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data .  The well planned statistical process allows us to have a peep of the overall picture from the sample.  Such a useful tool!  Even better, it can help us foresee the future. Have you ever wondered where sports betting companies’ offering odd coming forms? Do you know they always win? Guess...
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What is Randomness

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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...
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Frequentist probability

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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...
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