(a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
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2. Let X be a Chi-squared random variable with density function
fx(x) = exp (-;),
a
x > 0.
Suppose Y is independent of, and has the same distribution as, X.
(a) Let Z = VX. Show that the density function of Z is given by
Sale) = 2a exp (-)
z > 0.
Hence state the value of a.
Transcribed Image Text:2. Let X be a Chi-squared random variable with density function fx(x) = exp (-;), a x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = VX. Show that the density function of Z is given by Sale) = 2a exp (-) z > 0. Hence state the value of a.
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