The density of a random variable X is given by

x 0 < x < 1

f(x) = 2 - x 1 < x < 2

0 Otherwise

A) Find E l X l

B) Find the CDF of X. Write the following Probability in terms of the CDF of X and then compute it; P(X < 3/2 l X > 1/2)

C) Let X_1, X_2,......., X₁₀₀ be i.i.d random variables with the same distributions as X. What is the distribution of the number of X_i's such that 1/2 < X_i < 3/2

Write the expression for the chance that exactly 75 of the X_i's are below 0.5.