2. X is a random variable with support [-1, 2] and pdf fx (t) = ct' for te [-1, 2]. (a) Find the constant c. Sketch the pdf and cdf of X. (b) What are the values of E [X] and Var (X). (c) Define a new random variable Y = X2. What is the support of Y? What is the pdf of Y? Remark: Note that the function g (x) = c' is not monotone on the interval [-1, 2]. (d) Find E [X2] using the pdf of Y, namely, fy (t)