In finding and correcting errors in a software code (debugging) and determining the code’s reliability, computer software experts have noted the importance of the distribution of the time until the next coding error is found. Suppose that this random variable has a gamma distribution with parameter α = 1. One computer programmer believes that the mean time between finding coding errors is β = 24 days. Suppose that a coding error is found today.

a. Assuming that β = 24 days, find the probability that it will take at least 60 days to discover the next coding error.

b. If the next coding error takes at least 60 days to find, what would you infer about the programmer’s claim that the mean time between the detection of coding errors is β = 24 days? Why?