Consider Review Exercise 2.106 on page 95. There are two
Chapter , Problem 2.100(choose chapter or problem)
Consider Review Exercise 2.106 on page 95. 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 f(x, y) = 3 2 (x2 + y2), 0 x, y 1, 0, elsewhere. (a) Determine whether or not X and Y are independent. (b) It is of interest to know something about the proportion of Z = X + Y , the sum of the two proportions. Find E(X + Y ). Also find E(XY ). (c) Find Var(X), Var(Y ), and Cov(X, Y ). (d) Find Var(X + Y ).
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