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Let Y1, Y2, ... Y17 be a random sample size 17 from a N(0, o² = 12) distribution. Let X1 have a N(0, o² = 37) distribution. Assume that Y1, Y2,. Y17 are independent of X1. Let 17 17 U = (Y; - Y)² 17 i=1 1. Find c so that the distribution of cU is x2 (Chi-square). (Notice that U is not equal to S².) Also, give the degrees of freedom. (Justify your answer) 2. What is P(U > 44). (Give your answer with at least 4 significant digits)

Let Y1, Y2, ... Y17 be a random sample size 17 from a N(0, o² = 12) distribution. Let X1 have a N(0, o² = 37) distribution. Assume that Y1, Y2,. Y17 are independent of X1. Let 17 17 U = (Y; - Y)² 17 i=1 1. Find c so that the distribution of cU is x2 (Chi-square). (Notice that U is not equal to S².) Also, give the degrees of freedom. (Justify your answer) 2. What is P(U > 44). (Give your answer with at least 4 significant digits)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let Y1, Y2, ... Y17 be a random sample size 17 from a N(0, o2 = 12) distribution. Let X1 have a N (0, o² = 37) distribution. Assume that Y1, Y2, . .Y17 are independent of X1. Let 17 17 Y 17 ΣΥ U- ΣΥ-Ρ 1. Find c so that the distribution of cU is x² (Chi-square). (Notice that U is not equal to S?.) Also, give the degrees of freedom. (Justify your answer) 2. What is P(U > 44). (Give your answer with at least 4 significant digits)
Transcribed Image Text:Let Y1, Y2, ... Y17 be a random sample size 17 from a N(0, o2 = 12) distribution. Let X1 have a N (0, o² = 37) distribution. Assume that Y1, Y2, . .Y17 are independent of X1. Let 17 17 Y 17 ΣΥ U- ΣΥ-Ρ 1. Find c so that the distribution of cU is x² (Chi-square). (Notice that U is not equal to S?.) Also, give the degrees of freedom. (Justify your answer) 2. What is P(U > 44). (Give your answer with at least 4 significant digits)
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