Probability and Statistics

Question 1

Fundamental principle of counting states that

Answer 1

If a thing can be done m ways and another thing n ways then the two things can be done in mxn different ways

N = nm

Question 2

Permutation

Answer 2

nPr = n!/(n-r)!

All at once:

nPr = n!

Question 3

Ordered Arrangement of a finite number of elements

Answer 3

Permutation

Question 4

If two elements in a permutation of distinct elements are in reverse order relative to their normal or natural order, they constitute an ________

Answer 4

Inversion

Question 5

A permutation is said to be even if it contains an ____ number of inversions, it is odd if the number of inversions is _____

Answer 5

even, odd

Question 6

Cyclic Permutation

Answer 6

nPn = (n-1)!

Question 7

Permutations with identical elements

Answer 7

nPr = n! / (n-r)! p! q! …

p,q - # of similar elements

Question 8

Refers to a group of objects selected from a larger group in such a way that an object can be used more than once

Answer 8

Assortment

Assortment = (#choices for position 1)(#choices for position 2)(#choices for position 3) . . .

Question 9

Arrangement of the selection regardless of the order

Answer 9

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

all at once:
nCn = 1

Question 10

Relationship between Permutation and Combination

Answer 10

nCr = nPr / r!

Question 11

Numerical Assessment of likelihood expressed as a number between 0 and 1

Answer 11

Probability

Question 12

The father of the theory of probability

Answer 12

Gerolamo Cardano

Question 13

Controlled study whose outcome is uncertain but not entirely unknown

Answer 13

Experiment

Question 14

A recorded result of an experiment

Answer 14

Trial

Question 15

One of the possible results from an experiment trial

Answer 15

Outcome

Question 16

Some combination of possible outcomes in one experiment trial

Answer 16

Event

Question 17

Refers to the number of times a certain outcome will occur

Answer 17

Frequency of the outcome

Question 18

Relative Frequency of the outcome

Answer 18

RF = # occurences / # trials

Question 19

Probability that event occurs

Answer 19

Pe = # outcomes / total outcomes

Question 20

Probability that event does not occur

Answer 20

1 - Pe

Question 21

Mutually Exclusive Events

Answer 21

Pe or f = Pe + Pf

Question 22

Independent Events

Answer 22

Pe and f = Pe x Pf

Question 23

If there are two possible outcomes of an event and the possibilities of the outcome are independent and constant, the distribution of probabilities is called _____

Answer 23

Binomial distribution

Question 24

Binomial Distribution

Answer 24

P = nCr (p^r)(q^(n-r))

Question 25

Mean of Binomial Distribution

Answer 25

m = np n-# trials p-successful outcomes

Question 26

Variance of Binomial Distribution

Answer 26

Variance = npq n-# trials p-successful outcomes q-unsuccessful outcomes (1-p)

Question 27

Poisson Distribution

Answer 27

P(x) = (λ^x)(e^-λ) / x!

Question 28

Mean and Variance of Poisson Distribution

Answer 28

``` m = λ var = λ ```

Question 29

Poisson Distribution used as Approximation to Binomial Distribution when n>=2 p<=0.5 or when n>=100 np<=10

Answer 29

P(x) = ((np)^x)(e^-np) / x!

Question 30

Probability that an event occurs to probability that event does not occur

Answer 30

p:q

Question 31

Odds Against an event

Answer 31

Reciprocal for Odds for an event q:p

Question 32

The average amount a player can expect to win or lose on one play in any game of chance

Answer 32

Mathematical Expectation = Summation of (Probability of each possible outcome x payoff)

Question 33

Refer to data has been organized into groups or into frequency distribution

Answer 33

Grouped Data

Question 34

Data that has not been organized into groups

Answer 34

Ungrouped Data

Question 35

Refers to the individual group of items or scores used in a grouped frequency distribution or histogram. Also known as Bin Width

Answer 35

Class Interval

Question 36

Class Interval

Answer 36

(Highest value - Lowest value) / # of classes | Highest value - Lowest value) / (1+3.3log(n)

Question 37

Refers to a collection of all possible individuals, objects, scores, or measurements

Answer 37

Population

Question 38

Part of the population

Answer 38

Sample

Question 39

Refers to where quantitative data tend to cluster

Answer 39

Central Tendency

Question 40

Mean

Answer 40

Sum / # of elements

Question 41

Median

Answer 41

Middle of the arranged group of data (n+1 / 2 th) term in ordered arrangement if term is a non integer then it is midway between the two terms

Question 42

Mode

Answer 42

Most frequent value

Question 43

Geometric Mean

Answer 43

GM = nth root of (n1 x n2 x n3 . . .) GM = nth root of (value at end / value at beginning) - 1

Question 44

The reciprocal of arithmetic mean

Answer 44

Harmonic Mean

Question 45

An arithmetic mean that incorporates weighting to certain data elements

Answer 45

Weighted mean

Question 46

The measure uses weighting coefficients

Answer 46

Distance weighted estimator

Question 47

The arithmetic mean of data values after a certain number of proportion of the highest and lowest data values have been discarded

Answer 47

Truncated mean

Question 48

The arithmetic mean of the maximum and minimum values of a data set

Answer 48

Midrange

Question 49

The arithmetic mean of the of the two quartiles

Answer 49

Midhinge

Question 50

The weighted arithmetic mean of the median and two quartiles

Answer 50

Trimean

Question 51

The arithmetic mean in which extreme values are replaced by values closer to the median

Answer 51

Winsorised mean