Probability & Statistics

Question 1

also called combinatorial mathematics, the field
of mathematics concerned with problems of
selection, arrangement, and operation within a
finite or discrete system. Included is the closely
related area of combinatorial geometry.

Answer 1

Combinatorics

Question 2

states that if there are p ways to do one thing,
and q ways to do another thing, then there are pq
ways to do both things.

Answer 2

Fundamental Principle of Counting

Question 3

is a mathematical technique that determines the
number of possible arrangements in a set when
the order of the arrangements matters. (may order dapat, no. of ways)

Answer 3

Permutation

Question 4

Permutation Formula

Answer 4

nPr = n! /(n-r)!

Question 5

Permutation of Distinct Objects Formula (Identical)

Answer 5

P= n!/(a!b!c!)

Question 6

Circular Permutation

Answer 6

(n-1)!

Question 7

Circular Permutation in Space (ex. beads, necklace, can be flipped)

Answer 7

(n-1)!/2

Question 8

is a mathematical technique that determines the
number of possible arrangements in a collection of
items WHERE THE ORDER OF THE SELECTION DOES NOT MATTER

Answer 8

Combination

Question 9

Combination Formula

Answer 9

nCr= n!/ ((n-r)!(r!))

Question 10

is a counting technique that computes the
number of elements that satisfy at least one of
several properties while guaranteeing that
elements satisfying more than one property are
not counted twice.

Answer 10

Principle of Inclusion and Exclusion

Question 11

is a permutation of the elements of a set, such
that NO ELEMENT APPEARS IN ITS ORIGINAL POSITION.

Answer 11

Derangement

Question 12

Derangement Formula

Answer 12

[n!/e] then round up

Question 13

the ratio of the number of favorable outcomes to
the total number of outcomes.

Answer 13

Probability

Question 14

Probability Formula

Answer 14

P=E/S ; desired EVENT/SAMPLE SPACE
Alternative:
p+q=1
q=1-p

where q is the probability that it will not happen

Question 15

Binomial Distribution (ex. pair of dice)

Answer 15

P=nCr*(p^r)(1-p)^(n-r)

Question 16

Multinomial Distribution (ex. three players or more)

Answer 16

P= [n!/(a!b!c!)][p1^ap2^b*p3^c]

Question 17

Hypergeometric Distribution (ex.
‘Defective’ Items)

Answer 17

P= (mCa*nCb)/((m+n)C(a+b))

Question 18

Poisson Distribution (ex. failures)

Answer 18

P=(e^(-λ)*(λ)^x)/(x!)

where gamma= failures/time

Question 19

is defined as the likelihood of an event or
outcome occurring, based on the occurrence of a
previous event or outcome.

Answer 19

Conditional Probability

Question 20

is defined as the likelihood of an event or
outcome occurring, based on the occurrence of a
previous event or outcome.

uses phrases “if”, “given that”, “when”

Answer 20

Conditional Probability

Question 21

Conditional Probability

Answer 21

P(B|A) = [(P(A ∩ B))/P(A)]

Question 22

also known as the expected value, is the
summation or integration of a possible values from a random variable. It is also known as the product of the probability of an event occurring, denoted P(x), and the value corresponding with the actual observed occurrence of the event.

Answer 22

Mathematical Expectation

Question 23

Mathematical Expectation

Answer 23

EV=∑pW

Question 24

is a form of mathematical analysis that uses
quantified models, representations and synopses for a given set of experimental data or real-life studies.

Answer 24

Statistics

Question 25

is a single value that attempts to describe a set
of data by identifying the central position within
that set of data.

Answer 25

Measure of Central Tendency

Question 26

is the AVERAGE of the numbers.

Answer 26

Mean

Question 27

is the MIDDLE number in a sorted, ascending or
descending, list of numbers and can be more
descriptive of that data set than the average.

Answer 27

Median

Question 28

is the value that appears MOST FREQUENTLY in a
data set.

Answer 28

Mode

Question 29

the difference between the greatest and the least value of the data set.

Answer 29

Range

Question 30

Measure of Positions

Answer 30

Quartile Ranking; Decile Ranking; Percentile Ranking

Q1=P25
Q2=P5=D5
Q3=P75
Q4=P100=D10
D1=P10
D2=P20
D10=P100

Question 31

Range Formula

Answer 31

=max-min

Question 32

average of min & max

Answer 32

Midrange

Question 33

Midrange

Answer 33

=(max+min)/2

Question 34

is the average distance between each data value
and the mean.

Answer 34

Mean Absolute Deviation

Question 35

Sample Variance (σ_s^2)

Answer 35

σ_s^2=[∑(x-x-bar)^2/(n-1)]
(default)

Question 36

Population Variance (σ_p^2)

Answer 36

σ_p^2=[∑(x-x-bar)^2/(n)]

Question 37

Sample Standard Deviation (σ_s)

Answer 37

σ_s=sqrt[(∑(x-x-bar)^2/n-1]

Question 38

Population Standard Deviation (σ_p)

Answer 38

σ_p=sqrt[(∑(x-x-bar)^2/n]

Question 39

Mean Absolute Deviation (MAD)

Answer 39

MAD=(∑|x-x-bar|/n)