|Nov14-10, 04:12 PM||#1|
Q1. X and Y are two random variables that are independent and each one is uniform in the interval . The joint density is just 1 in the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and 0 outside. What is the conditional distribution of X + Y given X−Y ? What is the conditional expectation of X + Y given X − Y ?
Q2. If X and Y are independent and each one has an exponential distribution, the joint density is e−(x+y) if x, y ≥ 0 and 0 otherwise. What is the distribution of X − Y ? What is the distribution of X + Y given X − Y ?
Been stuck on this question for hours!
I got 1/2 for the first part of question 1 and 1 for the second part
and I got ∞ for the first part of question 2 and 0 for the second part
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