Show that the gamma density function with parameters (r, )

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QUESTION:

Show that the gamma density function with parameters (r, ) has a unique maximum at (r 1)/.

Questions & Answers

QUESTION:

Show that the gamma density function with parameters (r, ) has a unique maximum at (r 1)/.

ANSWER:

Step 1 of 3

Let  be a gamma random variable with parameters , with density function

Our task is to show that function

has a unique maximum at

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