1. With pen and paper or LaTeX, derive the maximum likelihood estimator for the rate (3)...

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1. With pen and paper or LaTeX, derive the maximum likelihood estimator for the rate (3) of the gamma distribution, I'(shape 3, rate). Show your work. Note that in RStudio, a and 3 are called shape and rate, respectively. The PDF is given below: = f(xla, B) = 3⁰ r(a) e-Br Hint: You are solving for 3 in terms of a. If you can separate the a and 8 terms, the a terms will disappear once you take the partial derivative with respect to 3. I would recommend not substituting 3 for a until you get your final result. 4 1. With pen and paper or LaTeX, derive the maximum likelihood estimator for the rate (3) of the gamma distribution, I'(shape 3, rate). Show your work. Note that in RStudio, a and 3 are called shape and rate, respectively. The PDF is given below: = f(xla, B) = 3⁰ r(a) e-Br Hint: You are solving for 3 in terms of a. If you can separate the a and 8 terms, the a terms will disappear once you take the partial derivative with respect to 3. I would recommend not substituting 3 for a until you get your final result. 4

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The given PDF is f x B x1 B Now for a sample 24 2an with x f x x p we have the joint distribution a... View the full answer