For each of the following families of distributions, explain whether it is an exponential family: Bernoulli(p), p E (0, 1) Ν μ. 1), μ ER N (µ,02), µ ER and o2 > 0

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter1: Functions
Section1.2: Functions Given By Tables
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| For each of the following families of distributions, explain whether it is an exponential family:
• Bernoulli(p), pE (0, 1)
. Ν (μ, 1), μ R
• N (µ,0²), µ E R and o² > 0
• Exponential(A), 1 > 0
. Uniform( [0, Θ]), Θ>0
Г (а, В), where a, B > 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:| For each of the following families of distributions, explain whether it is an exponential family: • Bernoulli(p), pE (0, 1) . Ν (μ, 1), μ R • N (µ,0²), µ E R and o² > 0 • Exponential(A), 1 > 0 . Uniform( [0, Θ]), Θ>0 Г (а, В), where a, B > 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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