MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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6. Suppose the common pmf of the random sample X₁, X₂, X, is Poisson with unknown
parameter > 0, with pmf:
-0
0 e
f(x|0) =
x = 0, 1, 2,
x!
Suppose also that the prior distribution of the parameter 0 is gamma with pdf:
α-1
f(0|a, λ) =
a > 0, λ > 0.
1
г(α)λa
...
(a) Find a Bayesian Estimator (BE) 0 of 0.
B
(b) Express 0 from part (a) as a function of the sample mean X and the mean λ of 0.
B
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Transcribed Image Text:6. Suppose the common pmf of the random sample X₁, X₂, X, is Poisson with unknown parameter > 0, with pmf: -0 0 e f(x|0) = x = 0, 1, 2, x! Suppose also that the prior distribution of the parameter 0 is gamma with pdf: α-1 f(0|a, λ) = a > 0, λ > 0. 1 г(α)λa ... (a) Find a Bayesian Estimator (BE) 0 of 0. B (b) Express 0 from part (a) as a function of the sample mean X and the mean λ of 0. B
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