Maximum likelihood estimator

Find the maximum likelihood estimator of for the probability function
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.

For calculating maximum likelihood estimator we have to calculate ,but I failed to calculate the likelihhod function L.

I knew the square root was of the 2 and Pi
BECAUSE this is a rv.

and the answer is the sample mean.

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

another ill-posed thread

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