#2. Suppose the probability density function for a random variable X equals the following: f(x) = 3x2 for {0 < x < 1}, f(x) = 0 otherwise. (a) Show that this is a valid pdf. (Hint: please refer to the two necessary conditions of a pdf. 1) The pdf must be non-negative for all x in the range of possible outcomes, over all possible outcomes must sum to 1, f ( x )=1 (b) Using integration, Find E(X) and the cdf, F(X). (c) Use F(X) to find the P(0.25 < X < 0.50). .) f ( x)0 . And 2) The integration