I'm really struggling with a question I've been working on, any help would be super appreciated.
If I were given a random sample $X_1,\dots,X_n$ from a distribution for which the joint density has the regular exponential form:
$$f(x_1,\dots,x_n;\theta)=\frac{b(x_1,\dots,x_n)\exp\big(c(\theta) {\textbf{T}}(x_1,\dots,x_n)\big)}{a(\theta)}$$
How would I go about showing that the maximum likelihood estimate (for the case where there is only one parameter and $c(\theta)=\theta$ ) satisfies the equation:
$$E\big[{\bf{T}} (X_1,\dots,X_n) \big] = {\bf{T}}(x_1,\dots,x_n)$$
My thoughts are to use the expectation of the score statistic equalling zero, but I can't seem to piece it together.
Thanks guys