anjuwaa
04-30-2010, 03:41 AM
This seems to be a tricky problem, I tried for hours to figure it out but failed miserably. I'd like to see what you guys have to say. Problem goes like this.
Let X1,X2,X3,......Xn be a random sample from a distribution with one of two pdfs. If θ=1, then f(x;θ = 1) = (1/√2π)*e^((-x^2)/2), -infinity < x < +infinity. If θ=2, then f(x;θ = 2) = 1/[π(1+X^2)],-infinity < x < +infinity. Find the maximum likelihood estimator of θ.
any comments on how to go about solving this will be highly appreciated.
Let X1,X2,X3,......Xn be a random sample from a distribution with one of two pdfs. If θ=1, then f(x;θ = 1) = (1/√2π)*e^((-x^2)/2), -infinity < x < +infinity. If θ=2, then f(x;θ = 2) = 1/[π(1+X^2)],-infinity < x < +infinity. Find the maximum likelihood estimator of θ.
any comments on how to go about solving this will be highly appreciated.