On your daily commute, you pass through five traffic lights. When you arrive at a traffic light, it is green with probability 3/4 and red with probability 1/4. If it is red, it causes you to be delayed by two minutes. What is the mean and variance of the total delay in your commute? (Answer: mean = 2.5, variance = 15/4). However I do not know how to arrive at them. Thank you Solution 1. Mean delay ; there are 5 traffic lights . delay at 1 = 2 mins . probability of this delay = 1/4; so for five lights the average delay time would be= (1/4)*2*5; = 2.5 mins; 2.variance = (summation xi^2 *pi - mean^2); xi = 2; pi=1/4; 2 mins delay for a red light; variance = (2*1/4*5+2*1/4*5 +.... 5 times)*2 - 25/4; = 10 -25/4; variance = 15/4;.