Let X be a random variable with probability density function:

f(x) =cx(1−x) 0≤x≤1, 0 otherwise.

(a) What is the value of c?
(b) What is the cumulative distribution function of X ? That is, find F (x) = P (X ≤ x).

(c) Use your answer in part (b) to find P (2 ≤ X ≤ 3).

(d) What is E[X]?

(e) What is Var(X)?