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(YX=1)= [0.297 (0) + 0.164(1)] / 0.461 = 0.356.
E(YX=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=1Y=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.
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 Spring '07
 Francisco
 Variance, Inflation, Unemployment, Mean, Covariance matrix

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