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5. Let X and Y have the joint p.d.f f(r, y) = cry'e-- for r > 0, y > 0, and zero otherwise. Recall the definition of Gamma function I(k) = 2*-le-#dr and the fact that F(k+ 1) = kT(k) for k > 1. a. Are X and Y independent? b. What is the value of c? Find the marginal p.d.f of X. C. d. Let X, ..., X be a random sample of size 32 from a population having the same distribution as that of X. Let Y = E X. Give an approximation for P(|Y - 64 > 8) based on the Central Limit Theorem. Note: P(Z < 1) = 0.8413

5. Let X and Y have the joint p.d.f f(r, y) = cry'e-- for r > 0, y > 0, and zero otherwise. Recall the definition of Gamma function I(k) = 2*-le-#dr and the fact that F(k+ 1) = kT(k) for k > 1. a. Are X and Y independent? b. What is the value of c? Find the marginal p.d.f of X. C. d. Let X, ..., X be a random sample of size 32 from a population having the same distribution as that of X. Let Y = E X. Give an approximation for P(|Y - 64 > 8) based on the Central Limit Theorem. Note: P(Z < 1) = 0.8413

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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5. Let X and Y have the joint p.d.f f(r, y) = cry'e-- for > 0, y > 0, and zero otherwise. Recall the definition of Gamma function I(k) = f a*-ledr and the fact that r(k + 1) = kF(k) for k > 1. !! a. Are X and Y independent? b. What is the value of c? €. Find the marginal p.d.f of X. d. Let X,..,X be a random sample of size 32 from a population having the same distribution as that of X. Let Y = EX. Give an approximation for P(|Y – 64| > 8) based on the Central Limit Theorem. Note: P(Z <1) = 0.8413 and P(Z < 2) = 0.9772 for Z~ N(0, 1)..
Transcribed Image Text:5. Let X and Y have the joint p.d.f f(r, y) = cry'e-- for > 0, y > 0, and zero otherwise. Recall the definition of Gamma function I(k) = f a*-ledr and the fact that r(k + 1) = kF(k) for k > 1. !! a. Are X and Y independent? b. What is the value of c? €. Find the marginal p.d.f of X. d. Let X,..,X be a random sample of size 32 from a population having the same distribution as that of X. Let Y = EX. Give an approximation for P(|Y – 64| > 8) based on the Central Limit Theorem. Note: P(Z <1) = 0.8413 and P(Z < 2) = 0.9772 for Z~ N(0, 1)..
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