STAT 225 Quiz 6

1. What is the standard deviation of his waiting time?
2. What is the probability that the rst order takes longer than 12 minutes?
3. Given that the rst order has not arrived in the rst 7 minutes, what is the probability that it takes
longer than 12 minutes?
R 1
1 fX(x)dx = 1
E[X] =
R 1
1 xfX(x)dx
V ar(X) = E[X2]  E[X]2
U Uniform(a; b)
FU(u) = ua
ba for a U b
E[U] = a+b
2
V ar(U) = (ba)2
12
X Exponential()
FX(x) = 1  ex
E[X] = 1

V ar(X) = 1
2

Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.

Instructors will not interpret questions for you.
The waiting time until a short-order cook gets his next order takes, on average, 6 minutes.
1. What is the standard deviation of his waiting time? (4 points)
2. What is the probability that the rst order takes longer than 10 minutes? (5 points)
3. Given that the rst order has not arrived in the rst 5 minutes, what is the probability that it takes longer than 10 minutes? (6 points)
R 1
1 fX(x)dx = 1
E[X] =
R 1
1 xfX(x)dx
V ar(X) = E[X2] E[X]2
U Uniform(a; b)
FU(u) = ua
ba for a U b
E[U] = a+b
2
V ar(U) = (ba)2
12
X Exponential()
FX(x) = 1  ex
E[X] = 1

V ar(X) = 1

2

Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit. Instructors will not interpret questions for you.

A neighborhood cat likes to wander around and make visits in the evening. He walks past Jane's window sometime equally likely over the interval between 7:30 p.m. and 7:55 p.m. and waits for Jane to wave at him. Jane checks for the cat at 8:00 every night. Assume the cat's behavior is independent of his previous actions.

1. Given that the cat has not arrived by 7:40 p.m., what is the probability he arrives before 7:50 p.m.?

2. What is the probability that the cat arrives before 7:35 p.m. the rst night and after 7:50 p.m. the
next?
3. What is the mean and variance of the cat's waiting time? (5 points)
R 1
1 fX(x)dx = 1
E[X] =
R 1
1 xfX(x)dx
V ar(X) = E[X2] E[X]2
U Uniform(a; b)
FU(u) = ua
ba for a U b
E[U] = a+b
2
V ar(U) = (ba)2
12
X Exponential()
FX(x) = 1  ex
E[X] = 1

V ar(X) = 1
2

Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.

Instructors will not interpret questions for you. A neighborhood cat likes to wander around and make visits in the evening. He walks past Sarah's window sometime equally likely over the interval between 7:25 p.m. and 7:55 p.m. and waits for Sarah to wave at him.
Sarah checks for the cat at 8:00 every night. Assume the cat's behavior is independent of his previous actions.

1. Given that the cat has not arrived by 7:45 p.m., what is the probability he arrives before 7:50 p.m.?

2. What is the probability that the cat arrives before 7:35 p.m. the rst night and after 7:45 p.m. the
next?
3. What is the mean and variance of the cat's waiting time? (5 points)
R 1
1 fX(x)dx = 1
E[X] =
R 1
1 xfX(x)dx
V ar(X) = E[X2]  E[X]2
U Uniform(a; b)
FU(u) = ua
ba for a U b
E[U] = a+b
2
V ar(U) = (ba)2
12
X Exponential()
FX(x) = 1  ex
E[X] = 1

V ar(X) = 1
2