# Suppose that Z is a standard normal random variable and that Y1 and Y2 are 2-distributed ## Problem 5.86 Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Problem 5.86

Suppose that Z is a standard normal random variable and that Y1 and Y2 are 2-distributed random variables with 1 and 2 degrees of freedom, respectively. Further, assume that Z, Y1, and Y2 are independent. a Define W = Z/ Y1. Find E(W) and V(W). What assumptions do you need about the value of 1? [Hint: W = Z(1/ Y1) = g(Z)h(Y1). Use Theorem 5.9. The results of Exercise 4.112(d) will also be useful.] b Define U = Y1/Y2. Find E(U) and V(U). What assumptions about 1 and 2 do you need? Use the hint from part (a).

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Elementary Statistics Notes Amanda Selly 8/29/2016  Mean: average  To find the mean you add up all the values and then divide by the number of values you have o Population mean: µ= x1+x2+x3+…+xN/N µ= Σx/N o Sample mean: ~x= x1+x2+x3+…+xn/n µ= Σx/n Please note that sample mean is indicated by an x with a bar on...

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##### ISBN: 9780495110811

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