Please do not use secondary source

1- 2- Let X1,X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values chumcmd p3 and variances 012, 0'22, and 033, respectively. a) If p1 = #2 = #3 = so and cf = 022 as? = 15 calculate Pm] s 200) and P(150 5 To 5 200)? b} Using the lui's and (II-'5 given in part (a), calculate both P(55 g f) and P(58 S X' S 62). c) If #1 = 404;2 = 50,,u3 = 60, of = 10, 022 = 12 and 05? = 14, calculate P(X1 + X2 + X3 3 160)and also P(X1 + X2 2 2X3). An experiment has the following probability distribution: _____ P00 ___\"- a) What are the expected value and standard deviation for a single randomly-chosen value of X? b) For a sample size n=50, what is the probability that the sample mean is less than 2.2