A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the proportion of time that the second line is in use. Suppose that the joint probability density function for (X, Y) is f(x,y)=cxy for e

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Chapter1: Combinatorial Analysis
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A service facility operates with two service lines. On a randomly selected day, let X be the
proportion of time that the first line is in use whereas Y is the proportion of time that the
second line is in use. Suppose that the joint probability density function for (X, Y) is
f(x,y)=cxy for e<x<3 and e<y<3.
a) (5p) Compute c.
b) (5p) Find marginal function of Y.
c) (6p) Find E(Y).
d) (6p) Find Var(Y)
e) (6p) Find cumulative distribution function for Y.
f) (5p) Are X and Y independent or not. Explain why.
g) (5p) P(x<2, y<1)=?
Transcribed Image Text:A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the proportion of time that the second line is in use. Suppose that the joint probability density function for (X, Y) is f(x,y)=cxy for e<x<3 and e<y<3. a) (5p) Compute c. b) (5p) Find marginal function of Y. c) (6p) Find E(Y). d) (6p) Find Var(Y) e) (6p) Find cumulative distribution function for Y. f) (5p) Are X and Y independent or not. Explain why. g) (5p) P(x<2, y<1)=?
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