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Example 15-6. Show that the m.g.f. of Y = log x², where x² follows chi-square distribution with n d.f., is given by My(t) = 2' (+ t) / r(n/2) If x1? and x2² are independent x²-variates each with n d.f. and U = %/ deduce that for positive integer k, E(U*) = r( + x) r( -k) / [F()]

Example 15-6. Show that the m.g.f. of Y = log x², where x² follows chi-square distribution with n d.f., is given by My(t) = 2' (+ t) / r(n/2) If x1? and x2² are independent x²-variates each with n d.f. and U = %/ deduce that for positive integer k, E(U*) = r( + x) r( -k) / [F()]

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 74E
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Example 15-6. Show that the m.g.f. of Y = log x², where x² follows chi-square distribution with n d.f., is given by My(t) = 2' T+ i) / r(n/2} If X1? and x2² are independent x²-variates each with n d.f. and U = %;"/X2, deduce that for positive integer k, %3D E(U')-r(플+)r(플-)/ [r(3)T 2 2
Transcribed Image Text:Example 15-6. Show that the m.g.f. of Y = log x², where x² follows chi-square distribution with n d.f., is given by My(t) = 2' T+ i) / r(n/2} If X1? and x2² are independent x²-variates each with n d.f. and U = %;"/X2, deduce that for positive integer k, %3D E(U')-r(플+)r(플-)/ [r(3)T 2 2
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