Answered: (✰✰✰✰) A certain random variable X has… | bartleby

Microeconomic Theory

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

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(✰✰✰✰) A certain random variable X has a Gamma distribution with scale parameter b and shape
parameters ẞ and s. This intimidating technical statement simply means that Pr(X < 0) = 0 and, for every
real x > 0,
Pr(X < x) = 1
88
(ẞB-1+ ebx)s
(We assume that b > 0, ẞ > 0, and s > 0.) Assuming for simplicity that ẞ = 2, find the probability density
p(x) for X. A piecewise answer is expected.
Answer: p(x) =
p(x) =
=
for x < 0,
for x ≥ 0.

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