You can easily generate random numbers in a spread-sheet that have an exponential distribution with a given mean. For example, to generate 200 such numbers from an exponential distribution with λ = 1/3, enter the formula = –3*LN(RAND()) in cell A4 and copy it to the range A5:A203. Then select the A4:A203 range, choose the Copy command, and choose the Paste Special command with the Values option. (This freezes the random numbers, so that they don’t change each time the spreadsheet recalculates.) Explore the properties of these numbers as follows.

a. Find the average of the 200 numbers with the AVERAGE function. What theoretical value should this average be close to?

b. Find the standard deviation of the 200 numbers with the STDEV function. What theoretical value should this standard deviation be close to?

c. Create a histogram of the random numbers, using about 15 categories, each of length 1, where the first category extends from 0 to 1. Does the histogram have the shape you would expect?

d. Suppose you collected the data in column A by timing arrivals at a store. The value in cell A4 is the time (in minutes) until the first arrival, the value in cell A5 is the time between the first and second arrivals, the value in cell A6 is the time between the second and third arrivals, and so on. How might you convince yourself that the inter-arrival times for this store are indeed exponentially distributed? What is your best guess for the arrival rate (customers per minute)?