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.