Suppose X is a random variable whose CDF is given by

Question

F(x) = 0, X<0
X^3, 0<X<1;
1, 1<X

Then the mean for this random variable is:

I don't understand how to do CDF (cumulitive distribution function) or how to get the mean of it. Thank You!

Answer 1

The average or mean of a distribution F(x) is the integral of F(x)dx
(which in this case = 1/4 when the limits are 0 and 1) divided by the width of the interval (which in this case = 1). So the answer is 1/4.