Let X1, X2,...Xn be i.i.d. Gamma(a,b) random variables where both a and b are unknown. Let T1= (X1 + X2 +...+ Xn)/n and T2 = (X21 + X22 +...+ X2n)/n be the first and second sample moments, respectively. Show the likelihood function of a and b.
So...I don't really understand what a likelihood function is. I believe it is the same algebraically as f(x1|a,b)*f(x2 | a,b)*...*f(xn | a,b), but I don't really know how to find this in terms of a and b. Any help is much appreciated. Thanks so much!