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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+ )

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 21E
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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
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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