Let X and Y be two independent random variable, uniformly distributed over the interval [-1, 1].-...

Transcribed Image Text:

Let X and Y be two independent random variable, uniformly distributed over the interval [-1, 1].- 1. Find P(0 < X < Y |X+Y > 0). Answer: 2. Find P(X >0| min(X, Y) > 0). Answer: 3. Find P(min(X, Y) >0|X>0). Answer: 4. Find P(min(X, Y)+ max(X, Y) > 1). Answer: 5. What is the pdf of Z := min(X, Y)? O fz(2) := (z - 1)/2 if z € (-1, 1) and fz(z) = 0 otherwise. O fz(2) := (1 – 2)/2 if z € (-1, 1) and fz(z) = 0 otherwise. O fz(2) := (z- 1)/2 for all z. O fz(2) := (1 – 2)/2 for all z. 6. What is the expected distance between X and Y? E [[X – Y|] = [Here, min(r, y) stands for the minimum of a and y. If necessary, round your answers to three decimal places.] Let X and Y be two independent random variable, uniformly distributed over the interval [-1, 1].- 1. Find P(0 < X < Y |X+Y > 0). Answer: 2. Find P(X >0| min(X, Y) > 0). Answer: 3. Find P(min(X, Y) >0|X>0). Answer: 4. Find P(min(X, Y)+ max(X, Y) > 1). Answer: 5. What is the pdf of Z := min(X, Y)? O fz(2) := (z - 1)/2 if z € (-1, 1) and fz(z) = 0 otherwise. O fz(2) := (1 – 2)/2 if z € (-1, 1) and fz(z) = 0 otherwise. O fz(2) := (z- 1)/2 for all z. O fz(2) := (1 – 2)/2 for all z. 6. What is the expected distance between X and Y? E [[X – Y|] = [Here, min(r, y) stands for the minimum of a and y. If necessary, round your answers to three decimal places.]