Question: 2. Jason is debugging his R code. The time it takes to find each error, in minutes, is exponentially distributed with rate parameter 0.

2. Jason is debugging his R code. The time it takes to

2. Jason is debugging his R code. The time it takes to find each error, in minutes, is exponentially distributed with rate parameter 0. Suppose Jason's code contains three errors, each search is independent, and he will search for them sequentially. Then the total time searching, T, follows a gamma distribution with shape parameter 3 and rate parameter 0. If we want to estimate Jason's debugging "rate," the likelihood function for when T = t > 0 and > 0 is therefore L(0; t) = 0 T(3) e-ot (a) (4 points) Find the maximum likelihood estimator, , for the rate parameter 0. Verify that it is a maximum with the second-derivative test. Note: if you cannot find mathematically, you can earn 2 points for this part by finding 0 numerically using the data from part (b). If you do this, include your R code. = (b) (2 points) Suppose it takes Jason a total of T the likelihood function and indicate the value of . 36 minutes to find the three errors. Plot

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