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) Construct the joint probability mass function (p.m.f.) of X and Y. b) From (a), produce the marginal p.m.f. of X and Y. Compute E(X). d) Calculate E(Y | X = 1) and Var(Y | X = 1). 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. a) Construct the joint probability mass function (p.m.f.) of X and Y. b) From (a), produce the marginal p.m.f. of X and Y. Compute E(X). d) Calculate E(Y | X = 1) and Var(Y | X = 1). Examine whether X and Y are independent. f) Let Z = X-2Y. Construct the probability mass function of Z, along with its domain.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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