QUIZ 8 - SOLUTION
Exercise 1
Two safety inspectors inspect a new building and assign it a safety score of 1, 2, 3, or 4. Suppose that
the random variable X is the score assigned by the first inspector and the random variable Y is the score
assigned by the

91.
102.
103.
A factory uses three production lines to manufacture cans of a
certain type. The accompanying table gives percentages of
nonconforming cans, categorized by type of nonconformance,
for each of the three lines during a particular time period.

FORMULAE
Combinatorics
Number of ways to complete an operation if there are n1 ways of completing step 1, n2 ways of
completing step 2, , nr ways of completing step r: 1 2
Number of permutations of k elements: ! = ( ) ( )
!
Number of permutations of 1 +

HOMEWORK PRACTICE 3
CONDITIONAL PROBABILITIES
PRACTICE
Exercise 1
Let A and B be two events associated with an experiment. Suppose that P(A) = 0.4 while
P(A B) = 0.7. Let P(B) = p.
(a) For what choice of p are A and B mutually exclusive?
(b) For what cho

HOMEWORK PRACTICE 1
COURSE PRACTICE
Exercise 1
Note that A in the textbook corresponds to the complement of set A (AC or as seen in class).
Exercise 2
An inspector visits 6 different machines during the day. In order to prevent operators from
knowing when

HOMEWORK PRACTICE 5
SOLUTION
PRACTICE
Exercise 1
Consider the workings of a queue of customers waiting for a teller in a bank during an eight-hour
workday. Classify each of the following random variables as either discrete or continuous.
(a) The number o

HOMEWORK PRACTICE 4
DISCRETE RANDOM VARIABLES
PRACTICE
Exercise 1
From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let X be the
number of defectives found. Obtain the probability distribution of X if
(a) the items are cho

HOMEWORK PRACTICE 1
Exercise 1
(a) A =
(b) (A B) (A B) = A
A
B
A
C
B
C
(c) (A B) C
(d) (B C) = B C
B
A
C
C
(e) (A B) C = (A B) since C (A B)
A
B
C
B
A
Exercise 2
An inspector varies the order of his visits to 6 different machines.
First inspection: 6 cho

HOMEWORK PRACTICE 7
MOMENTS & FUNCTIONS
Practice
Exercise 1
A manufacturer produces items such that 10 percent of items are defective and 90 percent are nondefective. If a defective item is produced, the manufacturer loses $1 while a non-defective item b

91.
102.
103.
A factory uses three production lines to manufacture cans of a
certain type. The accompanying table gives percentages of
nonconforming cans, categorized by type of nonconformance,
for each of the three lines during a particular time period.

HOMEWORK PRACTICE 2
COURSE PRACTICE
Exercise 1
2.62. A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If
a number is entered randomly, what is the probability that it is a valid number?
Exercise 2
2.64. A mess

HOMEWORK PRACTICE 5
RANDOM VARIABLES & MOMENTS
Exercise 1
Consider the workings of a queue of customers waiting for a teller in a bank during an eight-hour
workday. Classify each of the following random variables as either discrete or continuous.
(a) The

QUIZ 8
Notes:
1. Explain your reasoning clearly (it does not have to be lengthy) and define all your variables;
2. Your answer should be a response to the question (The probability of X is or P(Y) = );
3. Underline or circle your final answer.
4. Your sub

HOMEWORK PRACTICE 4 SOLUTION
PRACTICE
Exercise 1
From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let X be the
number of defectives found.
The sample space S of X is S = cfw_0, 1, 2, 3, 4, that is, we may pick any number o

HOMEWORK PRACTICE 8
JOINTLY DISTRIBUTED RANDOM
VARIABLES
Practice
Exercise 1
(a) Determine the value of c that makes the function f(x, y) = c (x + y) a joint probability mass function
(pmf) over the nine points with x = 1, 2, 3 and y = 1, 2, 3,
(b) Fill

HOMEWORK PRACTICE 8
JOINTLY DISTRIBUTED RANDOM
VARIABLES
Practice
Exercise 1
(a) Determine the value of c that makes the function f(x, y) = c (x + y) a joint probability mass function
(pmf) over the nine points with x = 1, 2, 3 and y = 1, 2, 3,
For f to

HOMEWORK 9 SOLUTION
Exercise 1
The number of people arriving at a fast-food restaurant is modeled as a Poisson random variable with
mean 60 customers/hour.
1. Let X be the number of people who arrive in an hour. X is a discrete random variable with
sample

MIDTERM 1 - SOLUTION
1. Quick questions all independent of one another (25 points)
a. License plates for cars in MO are in the following format:
LETTER LETTER DIGIT
LETTER DIGIT LETTER
Letters I and O are not used since they would too easily be confused w

MIDTERM 2 - SOLUTION
1. Quick questions all independent of one another (40 points)
a. A surveyor wishes to lay out a square region with each side having length L. However, because
of measurement error, he instead lays out a rectangle in which the north-so

HOMEWORK 7 SOLUTION
Practice
Exercise 1
A manufacturer produces items such that 10 percent of items are defective and 90 percent are nondefective. If a defective item is produced, the manufacturer loses $1 while a non-defective item brings a
profit of $5.

HOMEWORK PRACTICE 9
COMMON DISTRIBUTIONS
Exercise 1
The number of people arriving at a fast-food restaurant is modeled as a Poisson random variable
with mean 60 customers/hour.
1. Let X be the number of people who arrive in an hour. What is the expected