Probability & Statistics Flashcards
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.
Combinatorics
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.
Fundamental Principle of Counting
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)
Permutation
Permutation Formula
nPr = n! /(n-r)!
Permutation of Distinct Objects Formula (Identical)
P= n!/(a!b!c!)
Circular Permutation
(n-1)!
Circular Permutation in Space (ex. beads, necklace, can be flipped)
(n-1)!/2
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
Combination
Combination Formula
nCr= n!/ ((n-r)!(r!))
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.
Principle of Inclusion and Exclusion
is a permutation of the elements of a set, such
that NO ELEMENT APPEARS IN ITS ORIGINAL POSITION.
Derangement
Derangement Formula
[n!/e] then round up
the ratio of the number of favorable outcomes to
the total number of outcomes.
Probability
Probability Formula
P=E/S ; desired EVENT/SAMPLE SPACE
Alternative:
p+q=1
q=1-p
where q is the probability that it will not happen
Binomial Distribution (ex. pair of dice)
P=nCr*(p^r)(1-p)^(n-r)
Multinomial Distribution (ex. three players or more)
P= [n!/(a!b!c!)][p1^ap2^b*p3^c]
Hypergeometric Distribution (ex.
‘Defective’ Items)
P= (mCa*nCb)/((m+n)C(a+b))
Poisson Distribution (ex. failures)
P=(e^(-λ)*(λ)^x)/(x!)
where gamma= failures/time
is defined as the likelihood of an event or
outcome occurring, based on the occurrence of a
previous event or outcome.
Conditional Probability
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”
Conditional Probability
Conditional Probability
P(B|A) = [(P(A ∩ B))/P(A)]
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.
Mathematical Expectation
Mathematical Expectation
EV=∑pW
is a form of mathematical analysis that uses
quantified models, representations and synopses for a given set of experimental data or real-life studies.
Statistics
is a single value that attempts to describe a set
of data by identifying the central position within
that set of data.
Measure of Central Tendency
is the AVERAGE of the numbers.
Mean
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.
Median
is the value that appears MOST FREQUENTLY in a
data set.
Mode
the difference between the greatest and the least value of the data set.
Range
Measure of Positions
Quartile Ranking; Decile Ranking; Percentile Ranking
Q1=P25
Q2=P5=D5
Q3=P75
Q4=P100=D10
D1=P10
D2=P20
D10=P100
Range Formula
=max-min
average of min & max
Midrange
Midrange
=(max+min)/2
is the average distance between each data value
and the mean.
Mean Absolute Deviation
Sample Variance (σ_s^2)
σ_s^2=[∑(x-x-bar)^2/(n-1)]
(default)
Population Variance (σ_p^2)
σ_p^2=[∑(x-x-bar)^2/(n)]
Sample Standard Deviation (σ_s)
σ_s=sqrt[(∑(x-x-bar)^2/n-1]
Population Standard Deviation (σ_p)
σ_p=sqrt[(∑(x-x-bar)^2/n]
Mean Absolute Deviation (MAD)
MAD=(∑|x-x-bar|/n)
