Problem 3 (12 Points) In Muscat city, there are two types of services at a gas station. The gas station has a single regular lead-free pump with two hoses. In this context, A indicates the number of hoses being utilized on the self-service station at a certain time and B indicates the number of hoses on the full-service station utilizes at that time. The joint pmf of A and B i.e., fAB(A,B) is shown below. В 1 2 A 0.15 0.01 0.06 0.30 0.09 0.14 0.02 1 0.07 2 0.16 a. What is the probability that there is at most one self -service and at most one full- during service hose this event? (2.0) b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. (2.0) c. What is the probability that there is exactly one hose used in self-service during an event? (2.0) d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? (3.0) e. Are A and B independent events? Explain. (3.0)

Problem 3 (12 Points) In Muscat city, there are two types of services at a gas station. The gas station has a single regular lead-free pump with two hoses. In this context, A indicates the number of hoses being utilized on the self-service station at a certain time and B indicates the number of hoses on the full-service station utilizes at that time. The joint pmf of A and B i.e., fAB(A,B) is shown below. В 1 2 A 0.15 0.01 0.06 0.30 0.09 0.14 0.02 1 0.07 2 0.16 a. What is the probability that there is at most one self -service and at most one full- during service hose this event? (2.0) b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. (2.0) c. What is the probability that there is exactly one hose used in self-service during an event? (2.0) d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? (3.0) e. Are A and B independent events? Explain. (3.0)

Name: Problem 3 (12 Points)In Muscat city, there are two types of services
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Description: Problem 3 (12 Points)In Muscat city, there are two types of services at a gas station. The gas station has asingle regular lead-free pump with two hoses. In this context, A indicates the number ofhoses being utilized on the self-service station at a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 3 (12 Points)
In Muscat city, there are two types of services at a gas station. The gas station has a
single regular lead-free pump with two hoses. In this context, A indicates the number of
hoses being utilized on the self-service station at a certain time and B indicates the
number of hoses on the full-service station utilizes at that time. The joint pmf of A and B
i.e., fAB(A,B) is shown below.
1
2
A
0.15 0.01
0.06 0.30
0.09 0.14
0.02
1
0.07
2
0.16
a. What is the probability that there is at most one self -service and at most one full-
during
service
hose
this
event?
(2.0)
b. Give a word description of the event {A#1 and B#1}, compute the probability of
this event.
(2.0)
c. What is the probability that there is exactly one hose used in self-service during
an event?
(2.0)
d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)?
(3.0)
e. Are A and B independent events? Explain.
(3.0)

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