Exercise 4 Show that if X ~ Fp.g, then the corresponding probability density function is: r() x-1 f(a) = %3D ;x> 0 (21) p+q (1+ )
Exercise 4 Show that if X ~ Fp.g, then the corresponding probability density function is: r() x-1 f(a) = %3D ;x> 0 (21) p+q (1+ )
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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Transcribed Image Text:A distribution that comes up often in the design of experiments is:
Definition 1 Let U and V be independent random variables, U ~
X(P), and
V ~x'(q), then
U
X =
(20)
pV
has the F distribution with p,q degrees of freedom. One writes X ~ Fp.g.
Note that if T has the Student-t distribution with p degrees of freedom, then
T² ~ F1,p-
Exercise 4 Show that if X ~ Fp.q, then the corresponding probability density
function is:
r()
-1
2
f(x) =
ptq ; x>0
(21)
px
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