Maximum likelihood estimator

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October 20th 2009, 12:39 AM
roshanhero

Maximum likelihood estimator

Find the maximum likelihood estimator of $\theta$ for the probability function $f(x,\theta)=\frac{e^-0.5(x-\theta)^2}{\sqrt2\pi}$
Since I am very poor at latex,here are something that have gone missing like
1.It is the square root of 2pi at the denominator not only the square root of 2
2.It is e to the power -(x-theta)/2.
October 20th 2009, 12:47 AM
roshanhero

For calculating maximum likelihood estimator we have to calculate $\frac{\partial log\L}{\partial \theta} =0$ ,but I failed to calculate the likelihhod function L.
October 20th 2009, 01:27 AM
matheagle

I knew the square root was of the 2 and Pi
BECAUSE this is a $N(\theta ,1)$ rv.

and the answer is the sample mean.

and you forgot the square in your "explanation" in 2.

another ill-posed thread
October 20th 2009, 02:53 AM
roshanhero

I am still confused at calculating the likelihood function of the given p.d.f

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