A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.01 1 0.07 0.20 0.08 2 0.05 0.14 0.30 (d) Compute the marginal pmf of X. x 0 1 2 pX(x) Compute the marginal pmf of Y. y 0 1 2 pY(y) Using pX(x), what is P(X ≤ 1)? P(X ≤ 1) =

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.01 1 0.07 0.20 0.08 2 0.05 0.14 0.30 (d) Compute the marginal pmf of X. x 0 1 2 pX(x) Compute the marginal pmf of Y. y 0 1 2 pY(y) Using pX(x), what is P(X ≤ 1)? P(X ≤ 1) =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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x	0	1	2
p_X(x)

y	0	1	2
p_Y(y)

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A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.07 0.20 0.08 2 0.05 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|1) (b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.) y 0 1 2 pY|X(y|2) (d) Given that two hoses are in use at the…
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