Maximum likelihood error

1. Oct 29, 2008

sara_87

1. The problem statement, all variables and given/known data

pdf: f(x)=ax^(a-1) ; 0<x<1, a>0
estimate a by maximum likelihood

2. Relevant equations
let L be maximum likelihood
L=(a(x[1])^(a-1))(a(x[2])^(a-1))...(a(x[n])^(a-1))

3. The attempt at a solution

Im trying to make this into a nicer expression:
L=a^n... (now im stuck)

Any help would be v much appreciated.
Thank you.

2. Oct 29, 2008

Remember that if your density is $$f(x)$$, then the likelihood function for an i.i.d. sample is
$$L(x_1, \dots, x_n) = \prod_{i=1}^n f(x_i)$$
$$L(x_1, \dots, x_n) = \prod_{i=1}^n a x_i^{a-1} = a^n \prod_{i=1}^n x_i^{a-1}$$