Please answer the question on the top as it is related to excercise 16 which is written in bold. Hope that clarifies the question structure. 0 and a > 0) is defined in Exercise 16 ofSec. 5.7. Show...


Please answer the question on the top as it is related to excercise 16 which is written in bold.


Hope that clarifies the question structure.


The Pareto distribution with parameters x0 and a (X, > 0 and a > 0) is defined in Exercise 16 of<br>Sec. 5.7. Show that the family of Pareto distributions is a conjugate family of prior distributions for<br>samples from a uniform distribution on the interval [0, e], where the value of the endpoint e is<br>unknown.<br>16. It issaid that a random variable X has the Pareto distri-<br>bution with parameters x, and a (xo > 0 and a > 0) if X has<br>a continuous distribution for which the p.d.f. f(x|xq, «) is<br>as follows:<br>ax<br>f(x\xq, «) =<br>for x> Xo,<br>ra+1<br>for x < Xo-<br>Show that if X has this Pareto distribution, then the ran-<br>dom variable log(X/xo) has the exponential distribution<br>with parameter a.<br>

Extracted text: The Pareto distribution with parameters x0 and a (X, > 0 and a > 0) is defined in Exercise 16 of Sec. 5.7. Show that the family of Pareto distributions is a conjugate family of prior distributions for samples from a uniform distribution on the interval [0, e], where the value of the endpoint e is unknown. 16. It issaid that a random variable X has the Pareto distri- bution with parameters x, and a (xo > 0 and a > 0) if X has a continuous distribution for which the p.d.f. f(x|xq, «) is as follows: ax f(x\xq, «) = for x> Xo, ra+1 for x < xo-="" show="" that="" if="" x="" has="" this="" pareto="" distribution,="" then="" the="" ran-="" dom="" variable="" log(x/xo)="" has="" the="" exponential="" distribution="" with="" parameter="">

Jun 11, 2022
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