Gamma distribution

[dhs316]

Let X have a gamma distribution with parameters alpha=2 and theta. If x=2 is the mode of the distribution, find theta and P(X<9.488)

I'm completely stumped since this deals with mode instead of the usual. I think you have to take the derivative of the gamma function with respect to x. Then you would set it equal to 0. Then you set the game function equal to 2 (the mode). You have two equations, so two variables could be solved for. I'm not sure if this is the correct procedure. Please help.

The answers are: theta = 2, .95

Thanks.

 

[royhaas]

The mode of a gamma distribution, when it exists, is easily found by setting the derivative of the density to zero. This results in \(\displaystyle M = (\alpha -1)\theta\).