Q6(b) Let Y₂ ~ x² (n). The goal is to find the limiting distribution of Zn = (Yn-n) √2n as n →∞0. First, express the moment-generating function Mz, (t) of Zn in terms of the moment-generating function My, (t) of Yn. Then find ln(Mz„ (t). Use the fact ln(1 − x) = −x − x² /2 - x³/3 - x²/4 to show that as n → ∞, Mz, (t) converges to et²/2 and hence Zn converges to N(0, 1) as n → ∞o.
Q6(b) Let Y₂ ~ x² (n). The goal is to find the limiting distribution of Zn = (Yn-n) √2n as n →∞0. First, express the moment-generating function Mz, (t) of Zn in terms of the moment-generating function My, (t) of Yn. Then find ln(Mz„ (t). Use the fact ln(1 − x) = −x − x² /2 - x³/3 - x²/4 to show that as n → ∞, Mz, (t) converges to et²/2 and hence Zn converges to N(0, 1) as n → ∞o.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
solve part b please

Transcribed Image Text:Q6(a) Suppose X ~ x²(m), S = X+Y~x² (m+n), and X and Y are independent. Use moment-generating functions to show that
S-X~ x² (n).
Q6(b) Let Y₂ ~ x² (n). The goal is to find the limiting distribution of
Zn =
(Yn-n)
√2n
as n → ∞. First, express the moment-generating function Mz, (t) of Zn in terms of the moment-generating function My, (t) of Yn. Then
find ln(Mz, (t). Use the fact In(1-x) = -x-x² /2-x³/3-²/4 to show that as n →∞, Mz, (t) converges to et²/2 and hence Zn
converges to N(0, 1) as n → ∞.
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