Math 370X - Quiz 8Saumil PadhyaOctober 31, 2016Name Net ID1.The intensity of a hurricane is a random variable that is uniformly distributed on the interval[0, 3]. The damage from a hurricane with a given intensity y is exponentially distributedwith a mean equal to y.Calculate the variance of the damage from a random hurricane.(A) 1.73(B) 1.94(C) 3.00(D) 3.75(E) 6.002.A delivery service owns two cars that consume 15 and 30 miles per gallon. Fuel costs 3 pergallon. On any given business day, each car travels a number of miles that is independent ofthe other and is normally distributed with mean 25 miles and standard deviation 3 miles.Calculate the probability that on any given business day, the total fuel cost to the delivery servicewill be less than 7.Hint: For both cars, how much is the fuel cost per mile?(A) 0.13(B) 0.23(C) 0.29(D) 0.38(E) 0.4713.Let N denote the number of accidents occurring during one month on the northbound sideof a highway and let S denote the number occurring on the southbound side. Suppose thatN and S are jointly distributed as indicated in the table.N/S 0 1 2 3 or more0 0.04 0.06 0.10 0.041 0.10 0.18 0.08 0.032 0.12 0.06 0.05 0.023 or more 0.05 0.04 0.02 0.01Calculate Var (N|N+S = 2).(A) 0.48(B) 0.55(C) 0.67(D) 0.91(E) 1.254.The independent random variables X and Y have the same mean. The coefficients of variationof X and Y are 3 and 4 respectively.Calculate the coefficient of variation of 0.5(X+Y).(A) 5/4(B) 7/4(C) 5/2(D) 7/2(E)
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