Standard deviation | Variance | Statistics and Probability EP9

Standard deviation | Variance | Statistics and Probability EP9

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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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Law of large numbers

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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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