MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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) a. What is P(X = 1 and Y = 1)? b. Compute P(X ≤ 1 and Y ≤ 2). c. Compute the marginal pmf of X and of Y. d. Using px(x), what is P(X < 1)? e. Find ux x 0 1 2 0 .10 .08 .06 y 1 .04 .20 .14 2 .02 .06 .30
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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) a. What is P(X = 1 and Y = 1)? b. Compute P(X ≤ 1 and Y ≤ 2). c. Compute the marginal pmf of X and of Y. d. Using px(x), what is P(X < 1)? e. Find ux x 0 1 2 0 .10 .08 .06 y 1 .04 .20 .14 2 .02 .06 .30
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Step 1: Determining the given information
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Step 2: Finding the probability of X = 1 and Y = 1
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Step 3: Finding the probability of X less than or equal to 1 and Y less than or equal to 1.
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Step 4: Finding the marginal pmf of X and of Y
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Step 5: Finding the probability of X less than or equal 1 by using the marginal pmf of X
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Step 6: Finding the mean of x
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Solution
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