$$X_1,X_2,...,X_n \text{ i.i.d with density function}$$ $$f(x)=e^{-(x-\theta)}\;,x\ge\theta$$
What is the distribution of $\bar X$?
I gained m.g.f of $\bar X$. (by calculating $E[e^{1/n (X_1+\cdots+X_n)}])$
Result is ${(\frac n {n-t}})^{n}e^{ {t\theta} }$.
But I don't know distribution that has this m.g.f(moment generating function).
What is the distribution?
My process is wrong ?
Please answer...