STAT 5100 Final: STAT 5100 Iowa Final Exam c
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Please write your answers in the exam books provided: (5 points) the measurement of the diameter of a ball bearing is a normal random variable d with mean 1. 2cm and standard deviation 0. 1cm. An estimate of the volume of the ball bearing is v = . Find an approximation to the distribution of v : (10 points) let x and y have joint density f (x, y) =(c(2 x2 y2) A = {(u, v) : 0 u and u(1 + v2/u2) 1} The area of this set is |a| = /4. Find the density of x = v /u : (5 points) a random variable x has moment generating function. Find the mean and variance of x. for t < log(2) otherwise: (5 points) x1, . , xn is a random sample from a poisson population with mean. Find the limiting distribution of n(x n )/px n as n : (5 points) let x1, .