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PS1Soln

# PS1Soln - Solution to hw

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Problem Set 1 ECON 231W Spring 2010 Suggested Solutions 1. (a) 38.2 percent of the presidents were Republicans and were in the White House while Republicans controlled the House of Representatives. 44.2 percent of all presidents were Democrats. (b) E ( X ) = 0 . 558. E ( X | Y = 0) = 1 · P ( X = 1 | Y = 0)+0 · P ( X = 0 | Y = 0) = 1 · . 299+0 · . 701 = 0 . 299. E ( X ) gives you the unconditional expected value, while E ( X | Y = 0) is the conditional expected value. The second conditions on those periods during which Democrats had control of the House of Representatives, and ignores the other periods. (c) P ( Y = 0 | X = 1) = P ( Y =0 ,X =1) P ( X =1) = . 176 . 558 = . 315 (d) Demo Control of House Rep Control of House Total ( Y = 0) ( Y = 1) Demo President ( X = 0) 0.259 0.182 0.442 Rep President ( X = 1) 0.329 0.230 0.558 Total 0.588 0.412 1.00 Recall the deﬁnition of independence from Lecture 2: P ( Y = y | X = x ) = P ( Y = y ) . We can verify this using the above table. For example,

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PS1Soln - Solution to hw

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