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Recall that the exponential distribution with parameter A > 0 has density g (x) Ae, (x > 0). We write X Exp (A) when a random

Compute the Jeffreys prior TJ (A). If the answer is improper, enter your answer such that Tj (1) = 1. For A > 0, пу (А) — 10

Recall that the exponential distribution with parameter A > 0 has density g (x) Ae, (x > 0). We write X Exp (A) when a random variable X has this distribution. The Gamma distribution with positive parameters a (shape), B (rate) has density h (x) ox r e , (r > 0). and has expectation.We write X~ Gamma (a, B) when a random variable X has this distribution Suppose we have independent and identically distributed random variables X1,..., Xn, that we model as coming from an exponential ii.d distribution with some unknown parameter A > 0. In short, X1,..., Xn ^ Exp (A).
Compute the Jeffreys prior TJ (A). If the answer is improper, enter your answer such that Tj (1) = 1. For A > 0, пу (А) — 10 Li.d Exp (A). = 12. Recall X1,..., Xn X; In a particular scenario, we have n = 10 observations X1,...,X10 with i-1 Using the Bayesian approach with the Jeffreys prior TJ (A) computed above as the prior, compute the posterior distribution r (A|X1,..., X10) (Enter the posterior distribution in proportionality notation without worrying about the normalization factor.) п (A|X1,.., Xо) ох Compute Bayes' estimator, which is defined in lecture as the mean of the posterior distribution. (Enter your answer accurate to at least 3 decimal places.) Bayes
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Answen Given ExP basea of Noc the likeli ho dfunction given by Ti Ae L L (i e - Nocs the Paf (Poiebability dewsity fenction)Noc the fishe infal mation ,1(>) is given by I 2 Tyb VI enef Pri& No c the Pastenisn distoibuhion Xm?) Xil) m- Gromima ( Hnom

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