# Method of moments/maximum likelihood

1. Jun 3, 2006

### Gémeaux

I just needed some help with a few questions.

Consider N independent random variables having identical binomial distributions with parameters Θ and n= 3. If n0 of them take on the value 0, n1 of them take on the value 1, n2 of them take on the value 2 and n3 of them take on the value 3, use the method of moments to find a formula for estimating Θ.

Since X=nΘ, therefore X=3Θ. Now we need to find the mean of the random variables, which is (0*n0+1*n1+2*n2+3*n3)/N, since there are N random variables. So we get 3Θ = (n1+2n2+3n3)/N. Hence, Θ=(n1+2n2+3n3)/3N

Could someone tell me if I'm doing this right? Also, how would you use the method of maximum likelihood to estimate Θ?