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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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