Assume that X has density function f(x) = cx2 for 0 . x . 1 and f(x) = 0 otherwise.
(c) Determine c so that f(x) is a proper density function.
(b) Determine the cumulative distribution function of X. What is the probability P(0.1 . X . 0.5)?
(c) What are the expected value and the variance of this random variable?