Question: 3. Suppose Y is a random variable with pdf f(y)={2y, 0 3. Suppose Y is a random variable with pdf 2y, f(y) = O, In

3. Suppose Y is a random variable with pdf 2y, f(y) =

3. Suppose Y is a random variable with pdf f(y)={2y, 0

3. Suppose Y is a random variable with pdf 2y, f(y) = O, In the following, K 100000 and n 50. otherwise. (a) Find P (3/5 < Y < 11/15) by hand. (Hint: Recall c (bm+l am +1), where a, b, c are constants and m 1.) (1) (b) In R, a random sample of Y with size n can be generated as rbeta(n, 2, I). Find P(3/5 < Y < 11/15) by simulation by generating a random sample of Y with size K.

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