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Key ideas in probability and statistics illustrated on a simple problem

julienharbulot.com · 3,330 words · saved by 1 readers

This article aims to illustrate what are probability theory and statistical inference in simple terms using a simple to understand problem: drawing colored balls from an urn. Suppose that you have an urn containing red and green balls that you can’t distinguish otherwise than by their color. You can’t see inside the urn and you draw a ball without looking. Will you get a red or a green ball? We don’t know if you will get a red ball or a green ball. But if there are a thousand green balls and only one red ball, then it’s very likely that you will get a green ball. But how likely exactly? Probability theory aims to give a quantitative answer to that question. Given a problem as stated above, probability theory gives you the probability for a given outcome. The probability that you can compute for the outcome may or may not be useful for predicting the actual outcome. It’s usefulness primarily depends on how much you know about the problem. For instance, if you don’t know anything about t

This article aims to illustrate what are probability theory and statistical inference in simple terms using a simple to understand problem: drawing colored balls from an urn. Suppose that you have an urn containing red and green balls that you can’t distinguish otherwise than by their color. You can’t see inside the urn and you draw a ball without looking. Will you get a red or a green ball? We don’t know if you will get a red ball or a green ball. But if there are a thousand green balls and only one red ball, then it’s very likely that you will get a green ball. But how likely exactly? Probab

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