- Question 9 Answer Each Of The Following A In A Certain City 30 Percent Of The People Are Conservatives 50 Percent A 1 (220.29 KiB) Viewed 17 times
)Question 9 Answer each of the following. (a) In a certain city, 30 percent of the people are Conservatives, 50 percent are Liberals, and 20 percent are Independents. Records show that in a particular election, 65 percent of the Conservatives voted, 82 percent of the Liberals voted, and 50 percent of the Independents voted. If a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a Liberal? (b) Let X and Y be random variables with joint probability density function f(x,y) = { * 21 xºy2 for 0 < y < x < 1 otherwise. -3 Show that the conditional density for Y given X = x is g(y|x) = 3x-3y2, where 0 < y < x < 1, and 0 elsewhere. Hence calculate the conditional variance of Y given X = x, where 0 < x < 1. (c) Suppose that X has the uniform distribution on the interval (-1,1], so its proba- bility density function is — f(x) = { = 1/2 for -1 < x < 1 0 otherwise. Determine the cumulative density and the probability density functions for the random variable Y = = X? (d) Explain and discuss the method of moments approach to the estimation of the parameters of a statistical model.