Suppose the probability density function for a random

Question

Suppose the probability density function for a random variable X equals the following: 

f(x) = cx³ for {0 < x < 1}, f(x) = 0 otherwise. Where "c" stands for a constant value.

(a) Solve for the value of "c" that makes this a valid pdf. (Hint: please refer to the two necessary conditions of a pdf from the video introduction and .ppt.)

(b) Using integration, Find E(X) and the cdf, F(X). Use the value for "c" you found in (a).

(c) Use F(X) to find the P(0.25 < X < 0.50).