Module 3 Flashcards
Is a fundamental building block of
statistics
Probability
is the source of several very powerful
techniques used to represent randomness
Statistics
generate the random variate streams that drive a stochastic simulation
statistics
interpret the output data obtained from
conducting a stochastic simulation experiment.
statistics
collection of objects and usually denoted by capital letters
Set
objects of the set ( E )
Element
a set having no elements. ( or { } )
Null or Empty Set
There are no repeated occurrences of an element in the definition of
a set. (T OR F)
True
There are repeated occurrences of an element in the definition of
a set. (T OR F)
False
An object is either an element of a set or it is not. (T OR F)
True
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
countable
A set is called ____ if it is empty or if it has elements that can counted with the
counting process terminating.
finite
A set that is not finite is called _____
infinitr
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
subset
Two sets are said to be ______ if they have no common elements.
disjoint
The largest or all-encompassing set of elements under discussion in a given
situation is called the ___ denoted by U
universal / universal set
Two sets A and B are said to be _____, denoted A = B, if set A and set B
contained exactly the same elements
equal
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.
union
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
intersection
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
difference
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?
- {2,4,6,8,10}
- {4,10}
- {6,8,12}
- {2}
- {6,8}
A set of elements called the set X
domain
A set of elements called the set Y
codomain
A ________ that associates each element of
the domain set with exactly one element of the codomain set.
rule of correspondence f
For x E X and y E Y, a function is denoted by f:X → Y or f(x) = y. (T OR F)
True
Two functions are not equal if they have the same domain set, the
same codomain set and the same rule of correspondence.
False
Two functions are equal if they have the same domain set, the
same codomain set and the same rule of correspondence. (T OR F)
True
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
range
If the codomain of a function and the range of the function are
equal, then the function is said to _____
onto
If each element of the domain X maps to a unique element of the
codomain Y, then the function is said to be _______
one-to-one
A function f has an ______, denoted f^-1, if and only if f is one-to-one and onto
inverse
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)
True
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)
T
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
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)
T
