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) -
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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.
\[
\begin{array}{c|ccc}
p(x,y) & y = 0 & y = 1 & y = 2 \\
\hline
x = 0 & 0.10 & 0.03 & 0.02 \\
x = 1 & 0.07 & 0.20 & 0.07 \\
x = 2 & 0.06 & 0.14 & 0.31 \\
\end{array}
\]
(a) Given that \( X = 1 \), determine the conditional pmf of \( Y \)—i.e., \( P(Y = 0 | X = 1) \), \( P(Y = 1 | X = 1) \), \( P(Y = 2 | X = 1) \). (Round your answers to four decimal places.)
- \( P(Y = 0 | X = 1) \) = [ ]
- \( P(Y = 1 | X = 1) \) = [ ]
- \( P(Y = 2 | X = 1) \) = [ ]
(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.)
\[
\begin{array}{c|ccc}
y & 0 & 1 & 2 \\
\hline
P(Y = y | X = 2) & & & \\
\end{array}
\]
(c) Use the result of part (b) to calculate the conditional probability \( P(Y \leq 1 | X = 2) \). (Round your answer to four decimal places.)
- \( P(Y \leq 1 | X = 2) \) = [ ]
(d) Given that two hoses are in use at the full-service island, what is the conditional pm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94b64eaa-977b-4822-b8ab-e1a6b947c2d1%2F6a99ab90-05eb-4867-8d1c-10600037e736%2Fwa8vis_processed.png&w=3840&q=75)
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.
\[
\begin{array}{c|ccc}
p(x,y) & y = 0 & y = 1 & y = 2 \\
\hline
x = 0 & 0.10 & 0.03 & 0.02 \\
x = 1 & 0.07 & 0.20 & 0.07 \\
x = 2 & 0.06 & 0.14 & 0.31 \\
\end{array}
\]
(a) Given that \( X = 1 \), determine the conditional pmf of \( Y \)—i.e., \( P(Y = 0 | X = 1) \), \( P(Y = 1 | X = 1) \), \( P(Y = 2 | X = 1) \). (Round your answers to four decimal places.)
- \( P(Y = 0 | X = 1) \) = [ ]
- \( P(Y = 1 | X = 1) \) = [ ]
- \( P(Y = 2 | X = 1) \) = [ ]
(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.)
\[
\begin{array}{c|ccc}
y & 0 & 1 & 2 \\
\hline
P(Y = y | X = 2) & & & \\
\end{array}
\]
(c) Use the result of part (b) to calculate the conditional probability \( P(Y \leq 1 | X = 2) \). (Round your answer to four decimal places.)
- \( P(Y \leq 1 | X = 2) \) = [ ]
(d) Given that two hoses are in use at the full-service island, what is the conditional pm
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman