Module 3

Question 1

Is a fundamental building block of
statistics

Answer 1

Probability

Question 2

is the source of several very powerful
techniques used to represent randomness

Answer 2

Statistics

Question 3

generate the random variate streams that drive a stochastic simulation

Answer 3

statistics

Question 4

interpret the output data obtained from
conducting a stochastic simulation experiment.

Answer 4

statistics

Question 5

collection of objects and usually denoted by capital letters

Answer 5

Set

Question 6

objects of the set ( E )

Answer 6

Element

Question 7

a set having no elements. (  or { } )

Answer 7

Null or Empty Set

Question 8

There are no repeated occurrences of an element in the definition of
a set. (T OR F)

Answer 8

True

Question 9

There are repeated occurrences of an element in the definition of
a set. (T OR F)

Answer 9

False

Question 10

An object is either an element of a set or it is not. (T OR F)

Answer 10

True

Question 11

A set is said to be _____ if the elements of the set can be put in a one-to-one correspondence with the positive integer

Answer 11

countable

Question 12

A set is called ____ if it is empty or if it has elements that can counted with the
counting process terminating.

Answer 12

finite

Question 13

A set that is not finite is called _____

Answer 13

infinitr

Question 14

If every element of set A is also an element of set B, then A is said to be
contained in B and A is called a_____ of B denoted as A C_ B

Answer 14

subset

Question 15

Two sets are said to be ______ if they have no common elements.

Answer 15

disjoint

Question 16

The largest or all-encompassing set of elements under discussion in a given
situation is called the ___ denoted by U

Answer 16

universal / universal set

Question 17

Two sets A and B are said to be _____, denoted A = B, if set A and set B
contained exactly the same elements

Answer 17

equal

Question 18

The ____ of two sets A and B, denoted A U B, is the set consisting of all
elements that are contained either in set A or in set B.

Answer 18

union

Question 19

The _______ of two sets A and B, denoted A _ B, is the set consisting of all
elements that are contained in both sets A and B

Answer 19

intersection

Question 20

The ____ of two sets A and B, denoted A – B, is the set consisting of the
elements contained in set A that are not contained in set B. It should be
observed that, in general, A – B != B – A

Answer 20

difference

Question 21

U = { 2, 4, 6, 8, 10, 12 }
A = { 2, 4, 10 }
B = { 4, 6, 8, 10 }

What is A U B?
What is A intersect B?
What is A complement?
What is A – B?
What is B – A?

Answer 21

1. {2,4,6,8,10}
2. {4,10}
3. {6,8,12}
4. {2}
5. {6,8}

Question 22

A set of elements called the set X

Answer 22

domain

Question 23

A set of elements called the set Y

Answer 23

codomain

Question 24

A ________ that associates each element of
the domain set with exactly one element of the codomain set.

Answer 24

rule of correspondence f

Question 25

For x E X and y E Y, a function is denoted by f:X → Y or f(x) = y. (T OR F)

Answer 25

True

Question 26

Two functions are not equal if they have the same domain set, the same codomain set and the same rule of correspondence.

Answer 26

False

Question 27

Two functions are equal if they have the same domain set, the same codomain set and the same rule of correspondence. (T OR F)

Answer 27

True

Question 28

The ____ of a function f is the set of elements in the codomain Y that are associated with some element of the domain X under the rule of correspondence f

Answer 28

range

Question 29

If the codomain of a function and the range of the function are equal, then the function is said to _____

Answer 29

onto

Question 30

If each element of the domain X maps to a unique element of the codomain Y, then the function is said to be _______

Answer 30

one-to-one

Question 31

A function f has an ______, denoted f^-1, if and only if f is one-to-one and onto

Answer 31

inverse

Question 32

For function f:X → Y one-to-one and onto, the inverse is a function f -1 :Y → X such that f -1 [f(x)] = x for all x  X (T OR F)

Answer 32

True

Question 33

For m  0, the function is one-to-one and onto. Thus, it has an inverse function: x = f -1 (y) = (1/m)y – (b/m) (T OR F)

Answer 33

T

Question 34

For m = 0, the function becomes y = f(x) = b. All points in the domain map to a single point in the codomain. Range of function is the set {b}. Hence, function is neither one-to-one nor onto, and no inverse function exists

Answer 34

T

Question 35

For m = 0, the function becomes y = f(x) = b. All points in the domain map to a single point in the codomain. Range of function is the set {b}. Hence, function is neither one-to-one nor onto, and no inverse function exists (T OR F)

Answer 35

T