“expected value”的概念、定义、习题解题方法及翻译-数学辞典

单词

expected value

释义

expected value

The expected value E(X) of a random variable X is a value that gives the mean value of the distribution. For a discrete random variable X, E(X) = ∑pixi, where pi = Pr(X = xi). For a continuous random variable X,

where f is the probability density function of X. The following laws hold:

(i) E(aX+bY) = aE(X)+bE(Y).

(ii) When X and Y are independent, E(XY) = E(X)E(Y).

(iii) The law of total expectation: for a partition A1, A2, …, An of the sample space

The following is a simple example. Let X be the number obtained when a die is thrown. Let xi = i, for 1 ≤ i ≤ 6. Then $inline$ , for all i. So $inline$ .

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