Please answer parts a-d.

a.) For f(x)=cx^n for x in [0,1], and 0 otherwise, compute E[X^2].

b.) An urn has 8 red balls and 5 blue ones. Take one ball randomly, write down its color, put it back, repeat this experiment 6 times. What is the probability that exactly 5 of the colors you wrote down are red?

c.) What is the expected number of blue balls that you wrote down?

d.) What happens if the above experiment is not repeated 6 times, but until the first red ball is taken? In this case what is the expected number of repetitions needed?