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Bryx_Math > Probability and Statistics > Flashcards

Probability and Statistics Flashcards

1
Q

Fundamental principle of counting states that

A

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

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2
Q

Permutation

A

nPr = n!/(n-r)!

All at once:

nPr = n!

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3
Q

Ordered Arrangement of a finite number of elements

A

Permutation

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4
Q

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

A

Inversion

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5
Q

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

A

even, odd

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6
Q

Cyclic Permutation

A

nPn = (n-1)!

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7
Q

Permutations with identical elements

A

nPr = n! / (n-r)! p! q! …

p,q - # of similar elements

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8
Q

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

A

Assortment

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

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9
Q

Arrangement of the selection regardless of the order

A

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

all at once:
nCn = 1

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10
Q

Relationship between Permutation and Combination

A

nCr = nPr / r!

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11
Q

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

A

Probability

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12
Q

The father of the theory of probability

A

Gerolamo Cardano

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13
Q

Controlled study whose outcome is uncertain but not entirely unknown

A

Experiment

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14
Q

A recorded result of an experiment

A

Trial

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15
Q

One of the possible results from an experiment trial

A

Outcome

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16
Q

Some combination of possible outcomes in one experiment trial

A

Event

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17
Q

Refers to the number of times a certain outcome will occur

A

Frequency of the outcome

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18
Q

Relative Frequency of the outcome

A

RF = # occurences / # trials

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19
Q

Probability that event occurs

A

Pe = # outcomes / total outcomes

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20
Q

Probability that event does not occur

A

1 - Pe

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21
Q

Mutually Exclusive Events

A

Pe or f = Pe + Pf

22
Q

Independent Events

A

Pe and f = Pe x Pf

23
Q

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 _____

A

Binomial distribution

24
Q

Binomial Distribution

A

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

25
Q

Mean of Binomial Distribution

A

m = np

n-# trials
p-successful outcomes

26
Q

Variance of Binomial Distribution

A

Variance = npq

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

27
Q

Poisson Distribution

A

P(x) = (λ^x)(e^-λ) / x!

28
Q

Mean and Variance of Poisson Distribution

A 
m = λ
var = λ
29
Q

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

A

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

30
Q

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

A

p:q

31
Q

Odds Against an event

A

Reciprocal for Odds for an event

q:p

32
Q

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

A

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

33
Q

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

A

Grouped Data

34
Q

Data that has not been organized into groups

A

Ungrouped Data

35
Q

Refers to the individual group of items or scores used in a grouped frequency distribution or histogram.

Also known as Bin Width

A

Class Interval

36
Q

Class Interval

A

(Highest value - Lowest value) / # of classes

Highest value - Lowest value) / (1+3.3log(n)

37
Q

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

A

Population

38
Q

Part of the population

A

Sample

39
Q

Refers to where quantitative data tend to cluster

A

Central Tendency

40
Q

Mean

A

Sum / # of elements

41
Q

Median

A

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

42
Q

Mode

A

Most frequent value

43
Q

Geometric Mean

A

GM = nth root of (n1 x n2 x n3 . . .)

GM = nth root of (value at end / value at beginning) - 1

44
Q

The reciprocal of arithmetic mean

A

Harmonic Mean

45
Q

An arithmetic mean that incorporates weighting to certain data elements

A

Weighted mean

46
Q

The measure uses weighting coefficients

A

Distance weighted estimator

47
Q

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

A

Truncated mean

48
Q

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

A

Midrange

49
Q

The arithmetic mean of the of the two quartiles

A

Midhinge

50
Q

The weighted arithmetic mean of the median and two quartiles

A

Trimean

51
Q

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

A

Winsorised mean

Bryx_Math (9 decks)

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