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Assignment1_Answers

Assignment1_Answers - Assignment 2 Answers 1 a E[Y = 0.547...

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Assignment 2 - Answers 1. a) E[Y] = 0.547 or 54.7% of the quarters saw cyclical unemployment. E[X] = 0.461 or 46.1% of the quarters saw decreasing inflation rates. b) E(Y|X=1)= [0.297 (0) + 0.164(1)] / 0.461 = 0.356. E(Y|X=0)=0.711 You would expect the two conditional expectations to be the same. In general independence in means does not imply statistical independence, although the reverse is true. c) Probability of inflation to in crease if there is a positive unemployment = Pr(inflation to increase| positive unemployment) = Pr(X=0,Y=0)/ Pr(Y=0) = 0.156/0.453 = 0.344 Also doing the same calculations for a negative unemployment you will find that there is about 70% probability of inflation to increase if there is negative cyclical unemployment. d) Pr(decelerating inflation | Positive unemployment) = Pr(X=1|Y=0) = Pr(Y=0,X=1)/pr(Y=0) = 0.297/0.453 = 0.656 That implies there is a 65.6% probability of inflation to decelerate when there is positive cyclical unemployment. 2. To prove that i y k i i y p y 2 1 2 ) ( μ σ - = = is equal to 2 1 2 2 y k i i i y p y μ σ - = = Consider i y k i i y p y 2 1 2 ) ( μ σ - = = i y y k
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