Let X_{1}, X_{2},...X_{n }be i.i.d. Gamma(a,b) random variables where both a and b are unknown. Let T_{1}= (X_{1 }+ X_{2 }+...+ X_{n})/n and T_{2}= (X^{2}_{1 }+ X^{2}_{2 }+...+ X^{2}_{n})/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(x_{1}|a,b)*f(x_{2}| a,b)*...*f(x_{n}| 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!