Show that each of the following families is an exponential family (a) Normal family with either parameter or known (b) Gamma family with either parameter or known or both unknown (c) Beta family with either parameter or known or both unknown (d) Poisson family (e) Negative binomial family with r kn...

a i known hx 1 c 2 12 2 I 0 2 w 1 2 12 2 t 1 x x 2 ii 2 known hx ...

Show that each of the following families is an exponential family. (a) Normal family with either parameter

Question:

Show that each of the following families is an exponential family.
(a) Normal family with either parameter μ or σ known
(b) Gamma family with either parameter α or α known or both unknown
(c) Beta family with either parameter α or β known or both unknown
(d) Poisson family
(e) Negative binomial family with r known, 0 < p < 1