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.