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Assume that the following regression model was applied to historical quarterly data:

. Assume that the following regression model was applied to historical quarterly data:

ef,t = a0 + a1INTt + a2INFt 1 + εt

where ef,t = percentage change in the USD/JPY exchange rate in period t
INTt = interest rate differ¬ential between U.S. and Japan (iUS-iJAP) over period t
INFt 1 = inflation differential between U.S. and Japan (IUS-IJAP) in the previous period
a0, a1, a2 = regression coefficients
εt = error term

Assume that the regression coefficients were estimated as follows:
a0 = 0.0, a1 = 0.9, a2 = 0.8

Also assume that the inflation differential in the most recent period was 3%. The real interest rate differential in the upcoming period is forecasted as follows:

(iUS-iJAP) Probability
0% 30%
1 60%
2 10%

If Stillwater, Inc., uses this information to forecast the Japanese yen’s exchange rate, what will be the probability distribution of the yen’s percentage change over the upcoming period?

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