7. Probability computations using the exponential distribution An economist studied a large data set of Mexican consumer prices covering episodes of both high and low inflation. One of the goods in the study was milk. When the inflation rate was low, an average of 1.7 changes in the price of milk occurred each year. When the inflation rate was high, the price of milk changed more frequently-an average of 7.5 times each year. [Source: E. Etienne Gagnon, Price setting during low and high inflation: Evidence from Mexico, International Finance Discussion Papers, No. 896 (City: Board of Governors of the Federal Reserve System, 2007).] Let An equal the average number of milk-price changes in a d-month period when inflation is low. Let An equal the average number of milk-price changes in a 1-month period when inflation is high. A1 = 0.142 , and Ag = 0.625 Define X as the number of months between consecutive changes in the price of milk. X is exponentially distributed with A = An when inflation is low and A = My when inflation is high. When inflation is low, the mean number of months between consecutive price changes is 7.0 . When inflation is high, the mean number of months between consecutive price changes is 1.6 7 Now use the following Distributions tool to help you answer some of the questions that follow. When you use the tool, notice that you set the value of the mean , not the value of A. Poisson .15 .05 .00 0 1 2 3 4 5 6 7 8 0 10 11 12 13 14 15 The probability that the price of milk remains fixed for more than 5 months is when inflation is low and when inflation is high. If the probability that the price of milk stays the same for 2 months or less is about 0.71, is Mexico's inflation rate high or low? O Low O High If Mexico is in a low inflation episode, the variance of X is