Q: Let denote a random sample from the probability density function
for , and 0 otherwise.
a) Show that this density function is in the (one-parameter) exponential family and that is sufficient for (see previous exercise).
b) If , show that has an exponential distribution with mean .
Previews exercise mentioned in (a):
1) Suppose that is a random sample from a probability density in the (one-parameter) exponential family so that
, where is the indicator function and a and b do not depend on .
I think I am supposed to define each function in the density directly above for the orginal question; however, I am having a hard time doing so. Some direction would be great. Thanks.