Answered: A service station has both self-service…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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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	0.06	0.14	0.30

(a) Given that X = 1, determine the conditional pmf of Y—i.e., p_Y|X(0|1), p_Y|X(1|1), p_Y|X(2|1). (Round your answers to four decimal places.)

y	0	1	2
p_Y\|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
p_Y\|X(y\|2)

(c) 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.)

x	0	1	2
p_X\|Y(x\|2)

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