Given is a random variable X with probability density function f given by (x) = 0 for x 1, and f(x)=4x − 4x3 for 0 ≤ x ≤ 1. Determine the expectation and variance of the random variable 2X + 3 2....

Given is a random variable X with probability density function f given by
(x) = 0 for x <> 1, and f(x)=4x − 4x3 for 0 ≤ x ≤ 1. Determine the expectation and variance of the random variable 2X + 3

2. Given is a continuous random variable X whose distribution function F satisfies F(x) = 0 for x <> 1, and F(x) = x(2 − x) for 0 ≤ x ≤ 1. Determine E[X].