Question

A certain market has both an express checkout line and a
super-express checkout line. Let *X*_{1} denote the
number of customers in line at the express checkout at a particular
time of day, and let *X*_{2} denote the number of
customers in line at the superexpress checkout at the same time.
Suppose the joint pmf of *X*_{1} and
*X*_{2} is as given in the accompanying table.

x_{2} |
|||||

0 | 1 | 2 | 3 | ||

x_{1} |
0 | 0.08 | 0.06 | 0.04 | 0.00 |

1 | 0.07 | 0.13 | 0.05 | 0.06 | |

2 | 0.05 | 0.04 | 0.10 | 0.06 | |

3 | 0.00 | 0.03 | 0.04 | 0.07 | |

4 | 0.00 | 0.01 | 0.05 | 0.06 |

The difference between the number of customers in line at the
express checkout and the number in line at the superexpress
checkout is *X*_{1} − *X*_{2}.
Calculate the expected difference.

Answer #1

A certain market has both an express checkout line and a
super-express checkout line. Let X1 denote the
number of customers in line at the express checkout at a particular
time of day, and let X2 denote the number of
customers in line at the superexpress checkout at the same time.
Suppose the joint pmf of X1 and
X2 is as given in the accompanying table.
x2
0
1
2
3
x1
0
0.08
0.06
0.04
0.00
1
0.04
0.18...

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=x,Y=y) Y X 0 1 2 0 0.1 0.04 0.02 1 0.08...

An instructor has given a short quiz consisting of two parts.
For a randomly selected student, let X represent the number of
points earned on the first part and let Y represent the number of
points earned on the second part. Suppose that the joint pmf of X
and Y is given in the table below. Y 0 5 10 15 0 0.11 0.07 0.05
0.12 X 5 0.07 0.14 0.09 0.07 10 0.06 0.10 0.04 0.08 (a) Calculate
P(X...

An instructor has given a short quiz consisting of two parts.
For a randomly selected student, let X = the number of
points earned on the first part and Y = the number of
points earned on the second part. Suppose that the joint pmf of
X and Y is given in the accompanying table.
y
p(x, y)
0
5
10
15
x
0
0.03
0.06
0.02
0.10
5
0.04
0.15
0.20
0.10
10
0.01
0.15
0.13
0.01
(a)...

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 ...

An instructor has given a short quiz consisting of two parts.
For a randomly selected student, let X = the number of
points earned on the first part and Y = the number of
points earned on the second part. Suppose that the joint pmf of
X and Y is given in the accompanying table.
y
p(x,
y)
0
5
10
15
x
0
0.03
0.06
0.02
0.10
5
0.04
0.15
0.20
0.10
10
0.01
0.15
0.13
0.01
(a)...

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 1...

1. An electronic system has two different types of components in
joint operation. Let X1 and X2 denote the
Random Length of life in hundreds of hours of the components of
Type I and Type II (Type 1 and Type 2), respectively. Suppose that
the joint probability density function (pdf) is given by
f(x1, x2) = { (1/8)y1
e^-(x1 + x2)/2, x1 > 0,
x2 > 0
0 Otherwise.
a.) Show that X1 and X2 are
independent.
b.) Find E(Y1+Y2)...

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 ...

An instructor has given a short quiz consisting of two parts.
For a randomly selected student, let X = the number of points
earned on the first part and Y = the number of points earned on the
second part. Suppose that the joint pmf of X and Y is given in the
accompanying table. y p(x, y) 0 5 10 15 x 0 0.03 0.06 0.02 0.10 5
0.04 0.14 0.20 0.10 10 0.01 0.15 0.14 0.01 (a) Compute...

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