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Consider the data set on mercury in lakes in Maine (Hg.txt). Model the Hg levels as independent exponential random variables given θ, and use the Jeffery's prior on the rate θ.
(a) Use a new y node to get the posterior predictive probability P(y > .5/ y_{1,....} , y_{120}) (the probability of a dangerous mercury level) and also the extreme value P(y > 3.0/y_{1}, . . . , y_{120}).
(b) Compare the two probabilities above with the ones from the fitted exponential model and also with the empirical fractions from the data.
Attachment:- Hg.txt
(b) of Exercise 25 to calculate -2 · ln λ and test the null hypothesis = = = at the 0.05 level of signifi- cance. Explain why the number of degrees of freedom for this app
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