(f) For each of the following families of distributions, explain whet her it is an exponential family: Bernoulli(p), pE (0,1) N(u, 1). u ER N (u, a), ueR and o? >0 Exponential(A), A>0 Uniform((0, 0)), e>0 Г(а, В), wheте о, В >0 • Poisson(A), >0 • Binomial with parameters n and p • Binomial with n= 100 and other parameter being p Cauchy distribution centered around 0. .

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Chapter1: Functions
Section1.2: Functions Given By Tables
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(f)
For each of the following families of distributions, explain whet her it is an exponential family:
• Bernoulli(p), p E (0,1)
• N(u, 1). u e R
• N (u, a), ju ER and o?>0
• Exponential(A), A>0
• Uniform(J0, O), e>0
• (a, 3), where a, 3 >0
. Poisson(A), A >0
• Binomial with parameters n and p
• Binomial with n 100 and other parameter being p
• Cauchy distribution centered around 0.
Transcribed Image Text:(f) For each of the following families of distributions, explain whet her it is an exponential family: • Bernoulli(p), p E (0,1) • N(u, 1). u e R • N (u, a), ju ER and o?>0 • Exponential(A), A>0 • Uniform(J0, O), e>0 • (a, 3), where a, 3 >0 . Poisson(A), A >0 • Binomial with parameters n and p • Binomial with n 100 and other parameter being p • Cauchy distribution centered around 0.
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