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Exercise 6. Using the MGF given by Equation (24), deduce the expressions for the mean and variance we found earlier. Exercise 7. Prove the algebraic identity: (x – (+o²t))² , o?4 + ut + xt 25 2g2

Exercise 6. Using the MGF given by Equation (24), deduce the expressions for the mean and variance we found earlier. Exercise 7. Prove the algebraic identity: (x – (+o²t))² , o?4 + ut + xt 25 2g2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Exercise 6. Using the MGF given by Equation (24), deduce the expressions for the mean and variance we found earlier. Exercise 7. Prove the algebraic identity: 2g2 + xt = + ut 25 2g2
Transcribed Image Text:Exercise 6. Using the MGF given by Equation (24), deduce the expressions for the mean and variance we found earlier. Exercise 7. Prove the algebraic identity: 2g2 + xt = + ut 25 2g2
Example: The Gamma Distribution Suppose X ~ T(a, B), then eetz dx BaT(a) M(t) = (22) Now we do a little high school algebra. Define & = B Par. Then one may write 1-Bt Equation (22) as: M (t) = ()" J, 5aT(@) (23) dx One recognizes the integrand of Equation (23) as a r(a, 6) density, hence 1 M(1) = (r"() = (24) %3D (1 – Bt)a
Transcribed Image Text:Example: The Gamma Distribution Suppose X ~ T(a, B), then eetz dx BaT(a) M(t) = (22) Now we do a little high school algebra. Define & = B Par. Then one may write 1-Bt Equation (22) as: M (t) = ()" J, 5aT(@) (23) dx One recognizes the integrand of Equation (23) as a r(a, 6) density, hence 1 M(1) = (r"() = (24) %3D (1 – Bt)a
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