Homework Sourse1 Let X have a uniform distribution in the unit interval 0 1
1. Let X have a uniform distribution in the unit interval [0, 1], and let Y have an exponential distribution with parameter = 2. Assume that X and Y are independent. Let Z = X + Y .
(a) Find P(Y X).
(b) Find the conditional PDF of Z given that Y = y.
(c) Find the conditional PDF of Y given that Z = 3.
Solution
![1. Let X have a uniform distribution in the unit interval [0, 1], and let Y have an exponential distribution with parameter = 2. Assume that X and Y are indepen](/WebImages/16/1-let-x-have-a-uniform-distribution-in-the-unit-interval-0-1-1028716-1761532896-0.webp "1. Let X have a uniform distribution in the unit interval [0, 1], and let Y have an exponential distribution with parameter = 2. Assume that X and Y are indepen")
