Math 370X - Quiz 4Saumil PadhyaOctober 3, 2016Name Net ID1. Let X be a continuous random variable with density functionf(x) =|x|10for − 2 ≤ x ≤ 4Calculate the expected value of X.(A)15(B)35(C) 1(D)2815(E)1252. An insurer’s annual weather related loss, X, is a random variable with density functionf(x) =2.5 · 2002.5x3.5for x ≥ 200Calculate the difference between the 30th and 70th percentiles of X.(A) 35(B) 93(C) 124(D) 131(E) 29813.A recent study indicates that the annual cost of maintaining and repairing a car in a townin Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all itemsassociated with the maintenance and repair of cars (i.e., everything is made 20% moreexpensive), what will be the variance of the annual cost of maintaining and repairing a car?(A) 208(B) 260(C) 270(D) 312(E) 3744. Let X1, X2, X3be a random sample from a discrete distribution with probability functionp(x) =13for x = 023for x = 10 otherwiseDetermine the moment generating function, M(t), of Y =X1+X2+X3whereX1, X2, X3areindependent.(A)1927+827et(B) 1 + 2et(C)
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