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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. a) b) c) d) e) Construct the joint probability mass function (p.m.f.) of X and Y. From (a), produce the marginal p.m.f. of X and Y. Compute E(X). Calculate E(Y|X=1) and Var(Y|X=1). Examine whether X and Y are independent.

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. a) b) c) d) e) Construct the joint probability mass function (p.m.f.) of X and Y. From (a), produce the marginal p.m.f. of X and Y. Compute E(X). Calculate E(Y|X=1) and Var(Y|X=1). Examine whether X and Y are independent.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter9: Surfaces And Solids
Section9.CT: Test
Problem 14CT: Assume that a die used for gaming is in the shape of a regular octahedron. The faces are numbered...
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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. a) b) c) d) e) f) Construct the joint probability mass function (p.m.f.) of X and Y. From (a), produce the marginal p.m.f. of X and Y. Compute E(X). Calculate E(Y|X=1) and Var(Y|X=1). Examine whether X and Y are independent. Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.
Transcribed Image Text: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. a) b) c) d) e) f) Construct the joint probability mass function (p.m.f.) of X and Y. From (a), produce the marginal p.m.f. of X and Y. Compute E(X). Calculate E(Y|X=1) and Var(Y|X=1). Examine whether X and Y are independent. Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.
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