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. y p(x, y) 0 1 2 x 0 0.10 0.03 0.01 1 0.08 0.20 0.07 2 0.05 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|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.) y 0 1 2 pY|X(y|2) (c) Use the result of part (b) to calculate the conditional probability P(Y ≤ 1 | X = 2). (Round your answer to four decimal places.) P(Y ≤ 1 | X = 2) = (d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.) x 0 1 2 pX|Y(x|2)

Answer #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 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 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...

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 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 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 ...

5.1.8 Determine the value of c that makes the function f(x, y) =
c(x + y) a joint probability density function over the range 0 <
x < 3 and x < y < x + 2. c = (give the exact answer in the
form of fraction) Determine the following. Round your answers in
a-f to four decimal places.
a. P(X < 1, Y < 2) =
b. P(1 < X < 2) =
c. P(Y > 1) =...

Dan's Store has installed a self-service checkout counter, and
wishes to understand how this has affected customer service.
Shoppers arrive on average the rate of one every other minute
(Poisson distribution). Each shopper takes an average of 82 seconds
to use the checkout, and that time is exponentially
distributed.
a.
Calculate how long it takes, on average, for a shopper at the
self-service counter, including how long they wait in line and how
long it takes them to do their...

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...

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)...

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
0.17
0.20
0.10
10
0.01
0.15
0.11
0.01
(a)...

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
0.16
0.20
0.10
10
0.01
0.15
0.12
0.01
(a)...

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