Let random variable X have the cdf F given by:

F(x)= { 0 for x ≤ 0

(x^3/8) for 0< x<2

1 for x ≥ 2

1. Find P(X ≤ 2/3)

[(2/3)^3]/8 = .37

2. Find the probability density function for X

f(x) = x^2/16

3. Let random Variable Y = F(X). Find the Probability P(Y ≤ 2/3)

I just want to check my answers for parts 1 and 2. Can someone please help me with part 3