Instructions: Complete the following. Show all work. You can submit your answers on separate paper so that you do not need to download and print this exam.
(1)(10 points) Suppose the following is the PDF of a random variable X:
f (x) cex / 2,
where c is an unknown constant.
x 0
a.(5 points) What is the value of c that makes this a valid PDF?
b.(5 points) What is the CDF for this value of c?
(2)(10 points) Suppose the following is the PDF of a random variable X:
c.(5 points) Find E(X).
d.(5 points) Find Var(X).