MATH 302 Lecture Notes - Lecture 4: Random Variable

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30 Jul 2016
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Definition: expectation in simplest terms is taking each value, multiplying it by its probability and then adding all the results. Usually you need to find in questions related to profit loss, or insurance policy, about how much loss or profit you would make in the long run. So for example, if you play a game in which you win if you roll 1 on a dice. Is that fair? (10) * pr(rolling a 1) - (2)*(not rolling a 1) = (10* (1/6)) (2* (5/6)) = 0. This is a fair game, where you will break even in the long run. So, the idea of expectation is based on experimental probability. That is repeat an experiment a large number of times, and see the expected gains/losses. Let n1 be the value associated with x1, n2 the value associated with x2 and so on. X1n1 + x2n2 + x3n3 + x4n4 = the total sum of all values.

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