Does a presidential candidate from a certain party perform better when his party

Question

Does a presidential candidate from a certain party perform better when his party controls the House of Representatives? Consider the joint probability distribution of the random variable P, which equals 1 if a Republican is elected President and 0 if a Democrat is elected president, and H, which equals 1 when the House of Representatives is controlled by Republicans and 0 if controlled by Democrats, over the elections 1860-1996. You can think of these data as comprising a population which you want to describe, rather than a sample. Calculate the probability distributions of H and P. Interpret the joint probability f(H = 1, P = 1) and the probability f(P = 0). Compute E[P] and E[P|H = 0). Interpret these numbers. Are H and P independent P random variables or not? Compute E[P|H = 1] using the LIE and your result above. If you picked one of the Republican presidents at random, what is the probability that during his term the Democrats had control of the House of Representatives?

Explanation / Answer

a)

P(H=1,P=1) is the event when both president is of republicans and house of representative is controlled by republicans.

f(P=0) =44.20% =0.4420

b)E(p) =f(p=0)*0+fP(=1)*1 =55.80%=0.5580

similarly E(P|H=0) =0*41.2%+1*17.6%=17.6%=0.176

c) E(P|H=1) =0*3%+1*38.2%=38.2%=0.382

d)P(H=0|P=1) =0.176

P,H Dem House(H=0) Rep. House(H=1) f(P) Dem press(P=0) 41.20% 3.00% 44.20% Rep Press(P=1) 17.60% 38.20% 55.80% f(H) 58.80% 41.20% 100.00%

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