Let X, and X; be independent exponential random variables having pdfs f, (x) = e, x > 0 and fr,(x2) = e"", I3 > 0.Given thatY, = X,/XandY, = X, + X2.a. Find the joint pdf of Y, and Y2b. Find the marginal pdf of Y1.

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Let X, and X, be independent exponential random variables having pdfs f, (x1) = e=, x > 0 and fr,(x2) = e", 13 > 0. Given that Y = X,/X2 and Y = X, + Xg. a. Find the joint pdf of Y, and Y2 b. Find the marginal pdf of Y1.

Let X, and X, be independent exponential random variables having pdfs f, (x1) = e=, x > 0 and fr,(x2) = e", 13 > 0. Given that Y = X,/X2 and Y = X, + Xg. a. Find the joint pdf of Y, and Y2 b. Find the marginal pdf of Y1.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 41E

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Let X, and X; be independent exponential random variables having pdfs f, (x) = e, x > 0 and fr,(x2) = e"", I3 > 0.
Given that
Y, = X,/X
and
Y, = X, + X2.
a. Find the joint pdf of Y, and Y2
b. Find the marginal pdf of Y1.

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