Solve in digital format please Suppose that X|^ = ^ ~ Poisson(A) and that A ~Gamma(a, B) (A priori distribution).Prove using the Total Probability Theorem that theunconditional density of X has a distributionNegative binomial of parameters r = a and p =11+B'Hint: "Bring the integral to the gamma function".

Answered: Suppose that X|A = 1 ~ Poisson(A) and…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that X|A = 1 ~ Poisson(A) and that ^~ Gamma(a, B) (A priori distribution). Prove using the Total Probability Theorem that the unconditional density of X has a distribution Negative binomial of parameters r = a and p = 1+8· Hint: "Bring the integral to the gamma function".