A food truck park has two types of trucks: dessert trucks and drink trucks. Each truck can serve up to two customers simultaneously. Let A denote the number of customers being served at a dessert truck at a particular time, and let B denote the number of customers being served at a drink truck at the same time. The joint probability mass function (pmf) of A and B is given in the table below. p(a,b) b = 0 b = 1 b = 2 a = 0 0.12 0.05 0.03 a = 1 0.09 0.18 0.06 a = 2 0.04 0.10 0.33 (a) (4 pts) Compute P(A > B). (b) (4 pts) Compute P(A = 2 | B = 1). (c) (2 pts) Are A and B independent random variables? Explain. (d) (10 pts) Compute the marginal pmf of A and B. (e) (10 pts) Evaluate Cov(A, B), the covariance between A and B.

A food truck park has two types of trucks: dessert trucks and drink trucks. Each truck can serve up to two customers simultaneously. Let A denote the number of customers being served at a dessert truck at a particular time, and let B denote the number of customers being served at a drink truck at the same time. The joint probability mass function (pmf) of A and B is given in the table below. p(a,b) b = 0 b = 1 b = 2 a = 0 0.12 0.05 0.03 a = 1 0.09 0.18 0.06 a = 2 0.04 0.10 0.33 (a) (4 pts) Compute P(A > B). (b) (4 pts) Compute P(A = 2 | B = 1). (c) (2 pts) Are A and B independent random variables? Explain. (d) (10 pts) Compute the marginal pmf of A and B. (e) (10 pts) Evaluate Cov(A, B), the covariance between A and B.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 20E

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