Consider the U.S. population of registered voters, who may be Democrats, Republicans or independents. When surveyed about the war with ISIS, they were asked if they strongly supported war efforts, strongly opposed the war, or were neutral. Suppose that the proportion of voters in each category is given in Table P.8:

a. Find the "marginal" probability distributions for war attitudes and political party affiliation.

b. What is the probability that a randomly selected person is a political independent given that they are in favor of the war?

c. Are the attitudes about war with ISIS and political party affiliation statistically independent or not? Why?

d. For the attitudes about the war assign the numerical values \(A G A I N S T=1, N E U T R A L=2\), and \(I N\) \(F A V O R=3\). Call this variable WAR. Find the expected value and variance of WAR.

e. The Republican party has determined that monthly fundraising depends on the value of WAR from month to month. In particular the monthly contributions to the party are given by the relation (in millions of dollars) CONTRIBUTIONS \(=10+2 \times\) WAR. Find the mean and standard deviation of CONTRIBUTIONS using the rules of expectations and variance.

Transcribed Image Text:

TABLE P.8 Table for Exercise P.9 War Attitude Against Neutral In Favor Republican 0.05 0.15 0.25 Political Party Independent 0.05 0.05 0.05 Democrat 0.35 0.05 0