Question: A random variable X is distributed uniformly between 9 and 21. Let f(x) and F (x) be the probability density function and cumulative distribution function for X, respectively.

a) Find f(12), f (14), f(23), F(16), F(20), F(22).

b) Suppose 25 realizations of X are taken independently and their sum is computed. Find the probability that the sum exceeds 400. Reminder: the variance of a random variable uniformly distributed between a and b is equal to