A traffic light at a certain intersection is green 50% of the time, yellow 30% of the time, and red 20% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial. Let Y denote the number of days up to and including the third day on which a red light is encountered. a. Find P(Y = 4).b. Find the mean of Y. c. Find the variance of Y.