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A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. f(x,y) = 5 0. + +7y², 0sx,y≤1, elsewhere (a) Determine whether or not X and Y are independent. X and Y are not independent, since f(x,y) is not equal to g(x)h(y), where g(x) and h(y) are the marginal distributions of X and Y, respectively. (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). E(X+Y)= (Simplify your answer.)

A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. f(x,y) = 5 0. + +7y², 0sx,y≤1, elsewhere (a) Determine whether or not X and Y are independent. X and Y are not independent, since f(x,y) is not equal to g(x)h(y), where g(x) and h(y) are the marginal distributions of X and Y, respectively. (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). E(X+Y)= (Simplify your answer.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with this please parts b to d

A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. f(x,y) f 0₁ 5 x² + 7/7y²₁ 0≤x, y ≤ 1, elsewhere (a) Determine whether or not X and Y are independent. X and Y are not independent, since f(x,y) is not equal to g(x)h(y), where g(x) and h(y) are the marginal distributions of X and Y, respectively. (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). E(X+Y)= (Simplify your answer.)
Transcribed Image Text:A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. f(x,y) f 0₁ 5 x² + 7/7y²₁ 0≤x, y ≤ 1, elsewhere (a) Determine whether or not X and Y are independent. X and Y are not independent, since f(x,y) is not equal to g(x)h(y), where g(x) and h(y) are the marginal distributions of X and Y, respectively. (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). E(X+Y)= (Simplify your answer.)
(b) It is of interest to know something about the pro- portion of Z = X + Y, the sum of the two propor- tions. Find E(X+Y). Also find E(XY). (c) Find Var (X), Var(Y), and Cov(X, Y). (d) Find Var(X + Y).
Transcribed Image Text:(b) It is of interest to know something about the pro- portion of Z = X + Y, the sum of the two propor- tions. 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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