1 fv,.w(v, w) = %3D 27Vw(w+1) e¯v/2 v, w > 0. (c) Show that V and W are independent. State the distribution of V.
1 fv,.w(v, w) = %3D 27Vw(w+1) e¯v/2 v, w > 0. (c) Show that V and W are independent. State the distribution of V.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Only need help with Part C
Transcribed Image Text:(a) Let Z = vX. Show that the density function of Z is given by
fz(z) = 2a exp
2.
z > 0.
Hence state the value of a.
(b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is
%3D
given by
1
fv,w(v, w) =
-0/2
v, w > 0.
2TVw(w+1)
(c) Show that V and W are independent. State the distribution of V.
Transcribed Image Text:2. Let X be a Chi-squared random variable with density function
a
fx(x) =
exp
x > 0.
Suppose Y is independent of, and has the same distribution as, X.
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