3. Let X and Y be independent exponential random variables, both with λ = 1. (a) Find the cdf and pdf of W = 2X + Y. (b) Find the cdf and pdf of Z = min (X,Y). (c) Find the joint pdf of V = X + Y and W = 2X + Y. Sketch the area in v-w plane where fv,w(v, w) ± 0.

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3. Let X and Y be independent exponential random variables, both with λ = 1.
(a) Find the cdf and pdf of W = 2X + Y.
(b) Find the cdf and pdf of Z
=
min (X,Y).
(c) Find the joint pdf of V = X + Y and W = 2X + Y. Sketch the area in v-w plane where
fv,w(v, w) ± 0.
Transcribed Image Text:3. Let X and Y be independent exponential random variables, both with λ = 1. (a) Find the cdf and pdf of W = 2X + Y. (b) Find the cdf and pdf of Z = min (X,Y). (c) Find the joint pdf of V = X + Y and W = 2X + Y. Sketch the area in v-w plane where fv,w(v, w) ± 0.
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