The grade point averages (GPAs) for graduating seniors at a college are distributed as a continuous random variable X with pdf: f(x)=\left\{\begin{array}{ll}

k\left(1-(x-3)^{2}\right) & 2 \leq x \leq 4 \\

0 & \text { otherwise }

\end{array}\right. (a) Find the value of k.

(b) Find the probability that a GPA exceeds 3.

(c) Find the probability that a GPA is within .25 of 3.

(d) Find the probability that a GPA differs from 3 by more than .5

(e)What is the expected value and variance of X?