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(z,y) X Y (a) What is PX1 and Y P(X=1 and Y :1) = 1 0 0.10 0.03 0.01 0.06 0.20 0.07 0.05 0.14 0.34 2 1)? (b) Compute P(X<1 and Y≤1). P(X ≤ 1 and Y ≤1): (c) Give a word description of the event (X/0 and Y/0). O One hose is in use on both islands. O At least one hose is in use at both islands. O One hose is in use on one island. O At most one hose is in use at both islands. Compute the probability of this event. PLX and Yal
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(z,y) X Y (a) What is PX1 and Y P(X=1 and Y :1) = 1 0 0.10 0.03 0.01 0.06 0.20 0.07 0.05 0.14 0.34 2 1)? (b) Compute P(X<1 and Y≤1). P(X ≤ 1 and Y ≤1): (c) Give a word description of the event (X/0 and Y/0). O One hose is in use on both islands. O At least one hose is in use at both islands. O One hose is in use on one island. O At most one hose is in use at both islands. Compute the probability of this event. PLX and Yal
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...
Related questions
Question
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)
P(X:
(a) What is P(X= 1 and Y= 1)?
1 and Y 1) = [
0
P(X ≤ 1 and Y≤1)=
x
(b) Compute P(X ≤ 1 and Y≤1).
y
0
0.10 0.03 0.01
1 0.06 0.20 0.07
2
0.05 0.14 0.34
y
Py(V)
1
(c) Give a word description of the event { X 0 and Y#0}.
O One hose is in use on both islands.
O least one hose is in use at both islands.
O One hose is in use on one island.
O At most one hose is in use at both islands.
Compute the probability of this event.
P(X0 and Y 0) =
(d) Compute the marginal pmf of X.
0
0
Px(x)
Compute the marginal pmf of Y.
1
2
1
Using p(x), what is P(X < 1)?
P(X ≤1)=
2
(e) Are X and Y independent rv's? Explain.
OX and Y are not independent because P(x, y) ‡ px(z) - Py(y).
OX and Y are not independent because P(x, y) = Px(z) - Py (Y).
OX and Y are independent because P(x, y) = Px(z)-py (3).
OX and Y are independent because P(x, y) #Px(1) - PY (Y).
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
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON