# Joint Distributions

1. Jun 9, 2012

### Eulogy

1. The problem statement, all variables and given/known data
Let U,Y be independent random variables. Here U is uniformly distributed on (0,1) Where as
Y~0.25$\delta_{0}$ + 0.75$\delta_{1}$. Let X = UY. Find the Cdf and compute
P(0≤X≤2/3)

3. The attempt at a solution
Normally a question like this is fairly straightforward but I'm having trouble understanding how Y is distributed.

Last edited: Jun 9, 2012
2. Jun 9, 2012

### vela

Staff Emeritus
I take that to mean Y is a discrete random variable that assumes the value 0 25% of the time and the value 1 the remaining 75% of the time.