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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 ful rvice 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 0.01 1 0.07 0.20 0.07 0.06 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y-i.e., Pyix(01), Pyix(1|1), PYix(21). (Round your answers to four decimal places.) 2 0.0882 0.5882 0.2058

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 ful rvice 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 0.01 1 0.07 0.20 0.07 0.06 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y-i.e., Pyix(01), Pyix(1|1), PYix(21). (Round your answers to four decimal places.) 2 0.0882 0.5882 0.2058

A First Course in Probability (10th Edition)
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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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, у) 1 2 0.10 0.03 0.01 1 0.07 0.20 0.07 2 0.06 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y-i.e., pyix(0|1), pyıx(1|1), pyix(2|1). (Round your answers to four decimal places.) 1 PYix(y[1) 0.0882 0.5882 0.2058 (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 2 PYix(y12) 0.2692 0.1154 0.6154 (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) = 0.3846 (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 2 0.0250 0.1750 0.800
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. y p(x, у) 1 2 0.10 0.03 0.01 1 0.07 0.20 0.07 2 0.06 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y-i.e., pyix(0|1), pyıx(1|1), pyix(2|1). (Round your answers to four decimal places.) 1 PYix(y[1) 0.0882 0.5882 0.2058 (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 2 PYix(y12) 0.2692 0.1154 0.6154 (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) = 0.3846 (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 2 0.0250 0.1750 0.800
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