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A bowl contains twelve batteries of which four are new, five are used (working) and three are defective. Two batteries are randomly drawn without replacement. Let X denote the number of new batteries chosen and let Y denote the number of used batteries chosen. d) Calculate E(Y|X=1) and Var(Y|X=1). e) Examine whether X and Y are independent. f) Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.

A bowl contains twelve batteries of which four are new, five are used (working) and three are defective. Two batteries are randomly drawn without replacement. Let X denote the number of new batteries chosen and let Y denote the number of used batteries chosen. d) Calculate E(Y|X=1) and Var(Y|X=1). e) Examine whether X and Y are independent. f) Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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Question 3 A bowl contains twelve batteries of which four are new, five are used (working) and three are defective. Two batteries are randomly drawn without replacement. Let X denote the number of new batteries chosen and let y denote the number of used batteries chosen. d) Calculate E(Y|X=1) and Var(Y|X=1). e) Examine whether X and Y are independent. f) Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.
Transcribed Image Text:Question 3 A bowl contains twelve batteries of which four are new, five are used (working) and three are defective. Two batteries are randomly drawn without replacement. Let X denote the number of new batteries chosen and let y denote the number of used batteries chosen. d) Calculate E(Y|X=1) and Var(Y|X=1). e) Examine whether X and Y are independent. f) Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.
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