Exercise.
Let X be a random variable with probability density function:
f(x) =cx(5−x) 0≤x≤5, 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)?
Honor exercise.
Let X be a random variable with density function f(x)= ce^{-|x|}.
(a) What is the value of c ?
(b) Compute the density of the random variable Y=X^2
Research and Lecture notes 