Let X1, ,Xn be a random sample from a POI() distribution (i) Using Jeffreys prior, find the posterior distribution for (ii) Obtain the 95 credible interval for (iii) Obtain the HDP 95 interval for if n 3 and the actual observations are 2, 5, and 0 Hint The (1 )100 highest density interval is also the shortest (1 )100 credible interval Use Theorem 8 4 3 and statistical software

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Question: Let X1, ...,Xn be a random sample from a POI() distribution. (i) Using Jeffreys prior, find the posterior distribution for . (ii) Obtain the 95%

Let X1, ...,Xn be a random sample from a POI(θ) distribution. (i) Using Jeffreys prior, find the posterior distribution for θ. (ii) Obtain the 95% credible interval for

θ. (iii) Obtain the HDP 95% interval for θ if n = 3 and the actual observations are 2, 5, and 0. [Hint: The (1 − α)100% highest density interval is also the shortest

(1 − α)100% credible interval. Use Theorem 8.4.3 and statistical software.]

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