If f_Y(y;theta) = 2y/(1-theta^2), theta<=y<=1, find the maximum likelihood estimator for theta.
Any help would be great.
In this case you cannot differentiate.
The likelihood function is
And the largest we can make this is by letting the denominator be as small as possible.
So we want small or big.
BUT by the indicator function the largest can be is our smallest order stat.
Hence