# Question: Let and be independent and both exponentially distributed with Find the

Let and be independent and both exponentially distributed with

Find the PDF of Z = X –Y.

Find the PDF of Z = X –Y.

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For the joint CDF that is the product of two marginal CDFs, Fx,y (x, y) = Fx (x) Fy, as described in Exercise 5.4, show that the events {a< X < b}and {c < Y < d} are always independent for any constants a < b and c < d. Let and be independent and both uniformly distributed over (0, 2π. Find the PDF of Z = (X + Y) mod 2π. Suppose and are independent, Cauchy random variables with PDFs specified by Find the joint PDF of Z = X2 + Y2 and W = XY Repeat exercise 5.66 Suppose In figure 5.7 and P i = 1/3, i = 1, 2, 3. Determine the mutual information for this channel. If Can you give an interpretation for your result. A pair of random variables has a joint PDF specified by a) Find the constant c. b) Find Pr (X2 + Y2 > 1 / 4). c) Find Pr (X > Y).Post your question