7. 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 coffee. When the inflation rate was low, an average of 3.4 changes in the price of coffee occurred each year. When the inflation rate was high, the price of coffee changed more frequently-an average of 9.2 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).] The expected number of coffee-price changes in a 1-month period is when inflation is low and when inflation is high. Assume that y, the number of price changes in any 1-month period, is described by a Poisson probability distribution with a mean equal to one of the values you just calculated (depending on whether the inflation rate is high or low). of Then x, the number of months between consecutive price changes, is exponentially distributed with a mean of when inflation is high. when inflation is low and a mean Now use the following Distributions tool to help you answer some of the questions that follow. Poisson y .20 Mean = 3.0 .15 .10 .05 .00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x Now use the following Distributions tool to help you answer some of the questions that follow. Exponential Mean = 3.0 T ^ ^ ^ 0 2 6 8 10 12 14 16 The probability that the price of coffee remains fixed for more than 3 months is high. when inflation is low and when inflation is If the probability that the price of coffee stays the same for 2 months or less is about 0.44, is Mexico's inflation rate high or low? High O Low If Mexico is in a low inflation episode, the variance of x is