Suppose another variable X is continuous and its pdf is:

f(x)=x^3+ x^2- 2/3x + .75 0 < x < 1

A. For this question, you may take our word that f(x) is greater than or equal to

zero for all values of x in the domain. Prove the other condition that will make this a legitimate pdf.

b. Find P(X<1).

C. Find P(X>0.5)

D. Find P(X<0.5)

E. Find the mean of f(x)

F. Find the median of f(x).

G. SET UP BUT DO NOT CALCULATE the integral that finds us the variance of the amount of time students use to take the exam. Be sure to include the limits of integration.