Question
In: Statistics and Probability
1. A service station has both self-service and full-service islands. On each island, there is a...
1. 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 par- ticular time, and let Y denote the number of hoses on the full service island in use that time. The joint pmf of X and Y appears in the accompanying tabulation.
| 0 | 1 | 2 | |
| 0 | .10 | .04 | .02 |
| 1 | .08 | .20 | .06 |
| 2 | .06 | .14 | .30 |
a. WhatisP(X=1andY =1)?
b. ComputeP(X≤1andY ≤1).
c. Compute P(X ̸= 1 and Y ̸= 1).
d. Compute the marginal pmf of X and Y. Using pX(x), what is P(X ≤ 1)?
e. Are X and Y are independent? Explain.
2. Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable – X for the right tire and Y for the left tire, with joint pdf
?K(x2 +y2), 20≤x≤30, 20≤y≤30,
f(x,y) =
0, otherwise
a. What is the value of K?
b. What is the probability that both tires are underfilled?
c. What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Hint: Draw the shaded region first and then find the boundary of the integration.)
d. Determine the marginal pdf of X and Y . e. Are X and Y
independent? Explain.
f. Find E(X) and E(Y ).
Solutions
orchestra answered 2 years agoRelated Solutions
A service station has both self-service and full-service islands. On each island, there is a single...
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. y p(x,
y) 0 1 2 x 0 0.10 0.05 0.02 1...
A service station has both self-service and full-service islands. On each island, there is a single...
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.
y
p(x,
y)
0
1
2
x
0
0.10
0.03
0.01 ...
A service station has both self-service and full-service islands. On each island, there is a single...
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.
y
p(x,
y)
0
1
2
x
0
0.10
0.05
0.02 ...
A service station has both self-service and full-service islands. On each island, there is a single...
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.
y
p(x,
y)
0
1
2
x
0
0.10
0.05
0.01 ...
A service station has both self-service and full-service islands. On each island, there is a single...
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)
y
x
0
1
2
0
0.06
0.14
0.02
1
0.03...
A service station has both self-service and full-service islands. On each island, there is a single...
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.
y
p(x,
y)
0
1
2
x
0
0.10
0.03
0.02 ...
1.Consider a nation with two islands separated by water infestedwith fire-breathing dragons. Initially both islands...
1.Consider a nation with two islands separated by water infested
with fire-breathing dragons. Initially both islands are
self-sufficient and there are no cities. Suppose a dragon-whisperer
tames the dragons and harnesses them to serve as air cargo
carriers/a. The dragon re-purposing will cause trade if...b. If the dragon re-purposing causes trade, a trading city will
develop if...2.Explain the causes and the different kinds of agglomeration
economies. How does size of the city generate lower wages and
production cost?
Part A: The number of cars arriving at a self-service gasoline station during the last 50 hours...
Part A: The number of cars arriving
at a self-service gasoline station during the last 50 hours of
operation are as follows:
Number of Cars Arriving
Frequency
6
10
7
12
8
20
9
8
The following random numbers have been generated: 44, 30, 26,
09, 49, 13, 33, 89, 13, 37. Simulate 10 hours of arrivals at this
station. What is the average number of arrivals during this
period?
Part B: The time between arrivals at
a drive-through window of a...
A car wash has two stations, 1 and 2. The service time at station 1 is...
A car wash has two stations, 1 and 2. The service time at
station 1 is exponentially distributed with parameter λ1, and the
service time at station 2 is exponentially distributed with
parameter λ2.When a car arrives at the car wash, it begins service
at station 1, provided station 1 is free; otherwise, the car waits
until station 1 is available. Upon completing service at station 1,
the car then proceeds to station 2, provided station 2 is free;
otherwise,...
1. How would you design a service for self- recovery if a self-service failure in a...
1. How would you design a service for self- recovery
if a self-service failure
in a technology- generated service encounter were to
occur?
2. Why do service firms hesitate to offer a service guarantee?
3. Compare the
worst service experience you've ever had to the
best service experience you've ever had. What did the
service provider do differently to make these experiences stand out
in such contrast to one another? Consider all dimensions of the
service package in your answer....
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