Let X and Y be with joint probability density function given by: f(x, y) = (1...

Question

Question

Let X and Y be with joint probability density function given by:

f(x, y) = (1 / y) * exp (-y- (x / y)) {0 <x, y <∞} (x, y)

(a) Determine the (marginal) probability density function of Y.

(b) Identify the distribution and specify its parameter (s).

(c) Determine P (X> 1 | Y = y).

Answer 1

Answer #1

Given the joint PDF

b) The marginal PDF of is

b) The marginal PDF of is exponential with .

c) The conditional PDF ,

The probability,

Answer 2

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