3. An electronic system has one each of two different types of components in joint operation. Let Y, and Y, denote the random lengths of life of the components of type I and type II, respectively. The joint density function is given by 1 f(y1. Y2) = 0, ,Y1 > 0, y2 > 0 elsewhere a) Find P(Y, > 1, Y2 > 1) b) Are Y, and Y2 independent? c) What is the marginal distribution of Y,

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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3. An electronic system has one each of two different types of components in joint
operation. Let Y, and Y, denote the random lengths of life of the components of
type I and type II, respectively. The joint density function is given by
1
fV1, Y2) =
0,
,Y1 > 0, y2 > 0
elsewhere
a) Find P(Y, > 1, Y2 > 1)
b) Are Y, and Y, independent?
c) What is the marginal distribution of Y,
Transcribed Image Text:3. An electronic system has one each of two different types of components in joint operation. Let Y, and Y, denote the random lengths of life of the components of type I and type II, respectively. The joint density function is given by 1 fV1, Y2) = 0, ,Y1 > 0, y2 > 0 elsewhere a) Find P(Y, > 1, Y2 > 1) b) Are Y, and Y, independent? c) What is the marginal distribution of Y,
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