sta4321–finalexamprintname.docVIP

STA 4321 – Final Exam PRINT Name _____________ A game consists of 3 random numbers being selected from the Uniform density over the range [0,10] independently. That is X1,X2,X3 ~ iid U(0,10), with probability density function: Give the cumulative distribution function for this distribution and sketch it. The game pays off the largest of the three values, that is: X(3) = max(X1,X2,X3). Give the cumulative distribution function and probability density function for X(3). In a large class, on exam 1, the mean and standard deviation of scores were 72 and 15, respectively, For exam 2, the mean and standard deviation were 68 and 20, respectively. The covariance of the exam scores was 120. Give the mean and standard deviation of the sum of the two exam scores. Assume all students took both exams. The daily number of arrivals to a rural emergency room is a Poisson random variable with a mean of 100 people per day. Use the normal approximation to the Poisson distribution to obtain the approximate probability that 112 or more people arrive in a day. An airport baggage handling system is made up of a series of n=4 conveyor systems (each bag travels across conveyor 1, then conveyor 2, etc). Each conveyors’ times between unplanned maintenance are exponentially distributed with ?=1000 hours. Assume times to breakdown of the components are independent. The system must be shut down when any of the 4 conveyors breaks down. The probability density function for the smallest order statistic is: Give the mean and standard deviation of the times to breakdown (Hint: what is this distribution?). Give it in terms of numbers, not symbols. What is the probability the machine breaks down in less than 200 hours? A store sells washers and dryers. The joint distribution of the numbers of washers (W) and dryers (D) purchased by households entering the store is given below. p(w,d) d=0 d=1 w=0 0.6 0.1 w=1 0.1 0.2 Give the marginal distributions of washers sold and dryers sold. w p(w) d p(d) 0