If X and Y are two independent random variables, then
Question
If X and Y are two independent random variables, then
Solution
If X and Y are two independent random variables, then the following properties hold:
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The expected value of the product of X and Y is the product of their expected values. This can be mathematically represented as E(XY) = E(X)E(Y).
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The variance of the sum of X and Y is the sum of their variances. This can be mathematically represented as Var(X+Y) = Var(X) + Var(Y).
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The covariance of X and Y is zero. This can be mathematically represented as Cov(X,Y) = 0.
These properties are a direct result of the independence of the two random variables. Independence implies that the outcome of one variable does not affect the outcome of the other variable.
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