Let Ui, 1 i 3, be i.i.d. Uniform(0,1) random variables. Let X := min{1 i 3|Ui i/3}, and, given X = x, Y has Binomial(x,1/3) distribution. Write down the marginal pmf P [Y = y] of Y, and estimate E(Y^2) based on 100 iid copies of Y, to be generated by (a) inverse-transform method (Binomial (n, p) pmf at x {0, 1, . . . , n} may be computed as dbinom (x,n,p)). (b) composition method.

Using R.