For three categorical variables X, Y and Z: a. When Y is jointly independent of X and Z, show that X and Y are conditionally independent, given Z. b. Prove that mutual independence of X, Y and Z implies that X and Y are both marginally and conditionally independent. c. When X is independent of Y and Y is independent of Z, explain why X is not necessarily independent of Z.

For three categorical variables X, Y and Z: a. When Y is jointly independent of X and Z, show that X and Y are conditionally independent, given Z. b. Prove that mutual independence of X, Y and Z implies that X and Y are both marginally and conditionally independent. c. When X is independent of Y and Y is independent of Z, explain why X is not necessarily independent of Z.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 10TFE

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