Question

There are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X, Y ) is given by

Answer 1

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Answer:

A) The random variables X and Y are not independent

B) E(X) = 5/8 ; E(Y) = 5/8 ; E(X+Y) = 5/4 ; E(XY) = 3/8

C) E(X²) = 7/15 ; E(Y²) = 7/15 ; Var (X) = 73/960 ; Var(Y) = 73/960 ; Cov(X, Y) = - 1/64

D) Var(X+Y) = 29/240

Step-by-step explanation:

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