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. 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 μx p(x, y) x 0 1 2 0 .10 .08 .06 1 .04 .20 .14 2 .02 .06 .30
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. 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 μx p(x, y) x 0 1 2 0 .10 .08 .06 1 .04 .20 .14 2 .02 .06 .30
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
VIEWStep 2: Finding the probability of X = 1 and Y = 1
VIEWStep 3: Finding the probability of X less than or equal to 1 and Y less than or equal to 1.
VIEWStep 4: Finding the marginal pmf of X and of Y
VIEWStep 5: Finding the probability of X less than or equal 1 by using the marginal pmf of X
VIEWStep 6: Finding the mean of x
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