Joint Distribution: U,Y - Find P(0≤X≤2/3)

[Eulogy]

Homework Statement

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)

The Attempt at a Solution

Normally a question like this is fairly straightforward but I'm having trouble understanding how Y is distributed.

 

[vela]

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.