(✰✰✰✰) 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.
(✰✰✰✰) 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:(✰✰✰✰) 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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