There are two service lines. The random variables X and Y are the proportions of time...
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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) =(x² + y?), for 0< x, y <1, f(x,y)=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). 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) =(x² + y?), for 0< x, y <1, f(x,y)=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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Related Book For
Finite Mathematics and Its Applications
ISBN: 978-0134768632
12th edition
Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
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