Question 4 10 pts The random variableY has the Poisson distribution with a mean of 50. (a) What is the variance of Y? Answer 50 V (b) Compute the probability. P(Y > 60). Answer [Selcttl v (c) LetYI and Y; be two independent observations of Y. What is the variance of (Y1 + Y2)? Answer variance'l + Y2) = [59mm] V (d) Let Y1 and Y2 be two independent observations of Y. What is the variance of (Y1 7 Y; )? Answerrvariance'l 7 Y2) = [59mm] V Question 5 6 pts The time (in minutes) needed to repaira machine may be modelled bya random variable having the exponentiai distribution with a mean of 50 (minutes). Last year' there were 100 independent machine breakdowns. Let T denote the mean (average) repair time of the 100 machine breakdowns. (a) What is the variance of f? Answer: [SC'CHI V (b)What is the probabiiity that i is not ionger than 30 minutes? That is. compute 1:1? 3 30). Answer: [55'3\" V