a car service station, there are two service lines. The random variables X and Y are the portions of time that line 1 and line 2 are in use, respectively. The joint probability sity function for (X, Y) is given by f(z, w) = {,." S{(² + y³), 0sx s1;0sy s1 elsewhere. a) If Z=X+Y, the sum of two proportions, find Var(Z) b) Find Cov (X,Y)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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In a car service station, 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) ={6,"
S{(r² + y°), 0sx s1;0sy s1
elsewhere.
a) If Z=X+Y, the sum of two
proportions, find Var(Z)
b) Find Cov (X,Y)
Transcribed Image Text:In a car service station, 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) ={6," S{(r² + y°), 0sx s1;0sy s1 elsewhere. a) If Z=X+Y, the sum of two proportions, find Var(Z) b) Find Cov (X,Y)
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