Probability and Statistics Flashcards
Fundamental principle of counting states that
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
Permutation
nPr = n!/(n-r)!
All at once:
nPr = n!
Ordered Arrangement of a finite number of elements
Permutation
If two elements in a permutation of distinct elements are in reverse order relative to their normal or natural order, they constitute an ________
Inversion
A permutation is said to be even if it contains an ____ number of inversions, it is odd if the number of inversions is _____
even, odd
Cyclic Permutation
nPn = (n-1)!
Permutations with identical elements
nPr = n! / (n-r)! p! q! …
p,q - # of similar elements
Refers to a group of objects selected from a larger group in such a way that an object can be used more than once
Assortment
Assortment = (#choices for position 1)(#choices for position 2)(#choices for position 3) . . .
Arrangement of the selection regardless of the order
nCr = n!/(n-r)!r!
all at once:
nCn = 1
Relationship between Permutation and Combination
nCr = nPr / r!
Numerical Assessment of likelihood expressed as a number between 0 and 1
Probability
The father of the theory of probability
Gerolamo Cardano
Controlled study whose outcome is uncertain but not entirely unknown
Experiment
A recorded result of an experiment
Trial
One of the possible results from an experiment trial
Outcome
Some combination of possible outcomes in one experiment trial
Event
Refers to the number of times a certain outcome will occur
Frequency of the outcome
Relative Frequency of the outcome
RF = # occurences / # trials
Probability that event occurs
Pe = # outcomes / total outcomes
Probability that event does not occur
1 - Pe
Mutually Exclusive Events
Pe or f = Pe + Pf
Independent Events
Pe and f = Pe x Pf
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 _____
Binomial distribution
Binomial Distribution
P = nCr (p^r)(q^(n-r))
Mean of Binomial Distribution
m = np
n-# trials
p-successful outcomes
Variance of Binomial Distribution
Variance = npq
n-# trials
p-successful outcomes
q-unsuccessful outcomes (1-p)
Poisson Distribution
P(x) = (λ^x)(e^-λ) / x!
Mean and Variance of Poisson Distribution
m = λ var = λ
Poisson Distribution used as Approximation to Binomial Distribution when n>=2 p<=0.5 or when n>=100 np<=10
P(x) = ((np)^x)(e^-np) / x!
Probability that an event occurs to probability that event does not occur
p:q
Odds Against an event
Reciprocal for Odds for an event
q:p
The average amount a player can expect to win or lose on one play in any game of chance
Mathematical Expectation = Summation of (Probability of each possible outcome x payoff)
Refer to data has been organized into groups or into frequency distribution
Grouped Data
Data that has not been organized into groups
Ungrouped Data
Refers to the individual group of items or scores used in a grouped frequency distribution or histogram.
Also known as Bin Width
Class Interval
Class Interval
(Highest value - Lowest value) / # of classes
Highest value - Lowest value) / (1+3.3log(n)
Refers to a collection of all possible individuals, objects, scores, or measurements
Population
Part of the population
Sample
Refers to where quantitative data tend to cluster
Central Tendency
Mean
Sum / # of elements
Median
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
Mode
Most frequent value
Geometric Mean
GM = nth root of (n1 x n2 x n3 . . .)
GM = nth root of (value at end / value at beginning) - 1
The reciprocal of arithmetic mean
Harmonic Mean
An arithmetic mean that incorporates weighting to certain data elements
Weighted mean
The measure uses weighting coefficients
Distance weighted estimator
The arithmetic mean of data values after a certain number of proportion of the highest and lowest data values have been discarded
Truncated mean
The arithmetic mean of the maximum and minimum values of a data set
Midrange
The arithmetic mean of the of the two quartiles
Midhinge
The weighted arithmetic mean of the median and two quartiles
Trimean
The arithmetic mean in which extreme values are replaced by values closer to the median
Winsorised mean
