TIA Exam 1 #30

[STLIrish]

I see how the solution works this problem and it makes some sense but I don't know why they set it up this way. Really the whole question is confusing. Can anybody explain it?

[Hammer60]

Are you referring to the introduction of Y the gamma distribution?

[STLIrish]

Yes that and just the whole setup of the problem

[Hammer60]

MLE of an exponential is the mean of the data, E(x) = (X1 + ... + X10)/10.

However, we are given the distribution of an exponential with a mean of 1/lamda instead of the usual mean of lamda. So instead of finding the MLE of the normal parameter, we are finding the MLE of 1 divided by the normal parameter. We then use this to find the bias of the MLE of 1 divided by the normal parameter.

He introduces the gamma function to calculate the sum of exponential functions in the denominator. Im not exactly sure why, but you can't distribute the expected value over the random variables in the denominator.