Let X have the density fx(x) = c(2x + 1) for 0 ? x ? 4 and fx(x) = 0 otherwise, where c is a constant.
a) Find the value of c that makes this a valid probability density function.
b) Find p(2 ? x ? 3.5).
c) Write out Fx (x) for this random variable.
d) What is the average value of X?
e) Find Var(2X + 5).
f) Given that X is at least 2.5, what is the probability that it is less than 3.5?