$$f_T(t;B,C) = \frac{\exp(-t/C)-\exp(-t/B)}{C-B}$$
where our mean is $C+B$ and $t>0$.
so far i have found my log likelihood functions and differentiated them as follows:
$$dl/dB = \sum[t\exp(t/C) / (B^2(\exp(t/c)-\exp(t/B)))] +n/(C-B) = 0$$
i have also found a similar $dl/dC$.
I have now been asked to comment what you can find in the way of sufficient statistics for estimating these parameters and why there is no simple way of using Maximum Likelihood for estimation in the problem. I am simply unsure as to what to comment upon. Any help would be appreciated. Thanks, Rachel
Editor's Note: Given here is the probability density function $$ f_T (t;B,C) = \frac{{e^{ - t/C} - e^{ - t/B} }}{{C - B}}, \;\; t > 0, $$ where $B$ and $C$ are positive constants such that $C > B$. The mean is $C+B$. For the log likelihood function, see the last equation in my answer to this related question, and differentiate accordingly (with respect to $B$ and $C$).