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1. Suppose that X has an Exponential distribution with rate parameter λ = 1/4. Also suppose...

1. Suppose that X has an Exponential distribution with rate parameter λ = 1/4. Also suppose that given X = x, Y has a Uniform(x, x + 1) distribution.

(a) Sketch a plot representing the joint pdf of (X, Y ). Your plot does not have to be exact, but it should clearly display the main features. Be sure to label your axes.

(b) Find E(Y ).

(c) Find Var(Y ).

(d) What is the marginal pdf of Y ?

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