The wait time at a popular fast food restaurant is uniformly distributed between 2 and 10 minutes on average.
(a) Find the probability that you wait less than 4 minutes.
(b) Find the probability that you wait between 8 and 10 minutes.
(c) What is the expected wait time, and the variance of wait time?
(d) Explain why the answers to (a) and (b) are the same.
Hint: draw the probability density function for a Uniform random variable.