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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) = 0, (x²+y²), 0≤ x ≤ 1,0 ≤ y ≤ 1 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) = 0, (x²+y²), 0≤ x ≤ 1,0 ≤ y ≤ 1 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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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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) = 0, (x²+y²), 0≤ x ≤ 1,0 ≤ y ≤ 1 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).
Transcribed Image Text: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) = 0, (x²+y²), 0≤ x ≤ 1,0 ≤ y ≤ 1 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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