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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 Xa appears in the accompanying tabulation. P(x. Y) 1 2 0.10 0.03 0.02 1 0.07 0.20 0.07 0.06 0.14 0.31 (a) Given that X- 1, determine the conditional pmf of Y-L.e., PYx(011), PYx(1|1), PYLX(2|1). (Round your answers to four decimal places.) 2 (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.) PYxV12) (c) Use the result of part (b) to calculate the conditional probability P(Y S1|X- 2). (Round your answer to four decimal places.) P(Y S1|X- 2) -

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 Xa appears in the accompanying tabulation. P(x. Y) 1 2 0.10 0.03 0.02 1 0.07 0.20 0.07 0.06 0.14 0.31 (a) Given that X- 1, determine the conditional pmf of Y-L.e., PYx(011), PYx(1|1), PYLX(2|1). (Round your answers to four decimal places.) 2 (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.) PYxV12) (c) Use the result of part (b) to calculate the conditional probability P(Y S1|X- 2). (Round your answer to four decimal places.) P(Y S1|X- 2) -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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. p(x, y) 1 0.10 0.03 0.02 1 0.07 0.20 0.07 2 0.06 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y-i.e., pyjx(0|1), pyjx(1|1), PYjx(2|1). (Round your answers to four decimal places.) 2 PYIX(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.) 1 PYIX(y|2) (c) Use the result of part (b) to calculate the conditional probability P(Y < 1 | X = 2). (Round your answer to four decimal places.) P(Y < 1 | X = 2) = (d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.) 1 PX|Y(x|2) Need Help? Read It Watch It
Transcribed Image Text: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. p(x, y) 1 0.10 0.03 0.02 1 0.07 0.20 0.07 2 0.06 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y-i.e., pyjx(0|1), pyjx(1|1), PYjx(2|1). (Round your answers to four decimal places.) 2 PYIX(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.) 1 PYIX(y|2) (c) Use the result of part (b) to calculate the conditional probability P(Y < 1 | X = 2). (Round your answer to four decimal places.) P(Y < 1 | X = 2) = (d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.) 1 PX|Y(x|2) Need Help? Read It Watch It
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