- #1
Jamie_H
- 6
- 0
Homework Statement
Hi all, I missed the day of class where we went over likelihood functions, and I'm quite confused!
For example, let's say I have n Xis, where each Xi ~ Gamma(a,b), where a and b are unknown.
I want to find the likelihood function of a and b, but I don't think I really understand what this represents. (Please note - I am not looking for the maximum likelihood estimator! Just the likelihood function - when I attempt to find an explanation this seems to be the only thing that comes up)
Homework Equations
The class notes for that day explain that the likelihood function is the same as the pdf in this case, so
[(b^a)/(Gamma(a)]*x(a-1)e^(-bx), a fact verified with wikipedia. No idea why though!
The Attempt at a Solution
Truthfully, I'm not sure where to start here, so I don't have much of an attempt yet. I imagine this is fairly straight-forward/there is an obvious explanation as to why the pdf and likelihood function are the same, and I'm just missing it.
Thanks in advance - I really appreciate it! :)