Probability and statistics symbols
Probability and statistics:
Probability is a measure of the likeliness that an event will occur.
Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.It deals with all aspects of data including the planning of data collection in terms of the design of surveysand experiments. When analyzing data, it is possible to use one of two statistics methodologies:descriptive statistics or inferential statistics.
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
P(A) | probability function | probability of event A | P(A) = 0.5 |
P(A ∩ B) | probability of events intersection | probability that of events A and B | P(A∩B) = 0.5 |
P(A ∪ B) | probability of events union | probability that of events A or B | P(A∪B) = 0.5 |
P(A | B) | conditional probability function | probability of event A given event B occured | P(A | B) = 0.3 |
f (x) | probability density function (pdf) | P(a ≤ x ≤ b) = ∫ f (x)dx | |
F(x) | cumulative distribution function (cdf) | F(x) = P(X ≤ x) | |
μ | population mean | mean of population values | μ = 10 |
E(X) | expectation value | expected value of random variable X | E(X) = 10 |
E(X | Y) | conditional expectation | expected value of random variable X given Y | E(X | Y=2) = 5 |
var(X) | variance | variance of random variable X | var(X) = 4 |
σ^{2} | variance | variance of population values | σ^{2 }= 4 |
std(X) | standard deviation | standard deviation of random variable X | std(X) = 2 |
σ_{X} | standard deviation | standard deviation value of random variable X | σ_{X}_{ }= 2 |
median | middle value of random variable x | ||
cov(X,Y) | covariance | covariance of random variables X and Y | cov(X,Y) = 4 |
corr(X,Y) | correlation | correlation of random variables X and Y | corr(X,Y) = 0.6 |
ρ_{X,Y} | correlation | correlation of random variables X and Y | ρ_{X,Y} = 0.6 |
∑ | summation | summation – sum of all values in range of series | |
∑∑ | double summation | double summation | |
Mo | mode | value that occurs most frequently in population | |
MR | mid-range | MR = (x_{max}+x_{min})/2 | |
Md | sample median | half the population is below this value | |
Q_{1} | lower / first quartile | 25% of population are below this value | |
Q_{2} | median / second quartile | 50% of population are below this value = median of samples | |
Q_{3} | upper / third quartile | 75% of population are below this value | |
x | sample mean | average / arithmetic mean | x = (2+5+9) / 3 = 5.333 |
s_{ }^{2} | sample variance | population samples variance estimator | s^{ }^{2} = 4 |
s | sample standard deviation | population samples standard deviation estimator | s = 2 |
z_{x} | standard score | z_{x} = (x-x) / s_{x} | |
X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) |
N(μ,σ^{2}) | normal distribution | gaussian distribution | X ~ N(0,3) |
U(a,b) | uniform distribution | equal probability in range a,b | X ~ U(0,3) |
exp(λ) | exponential distribution | f (x) = λe^{–λx} , x≥0 | |
gamma(c, λ) | gamma distribution | f (x) = λ c x^{c-1}e^{–λx} / Γ(c), x≥0 | |
χ^{ 2}(k) | chi-square distribution | f (x) = x^{k}^{/2-1}e^{–x/2} / ( 2^{k/2 }Γ(k/2) ) | |
F (k_{1}, k_{2}) | F distribution | ||
Bin(n,p) | binomial distribution | f (k) = _{n}C_{k} p^{k}(1-p)^{n-k} | |
Poisson(λ) | Poisson distribution | f (k) = λ^{k}e^{–λ} / k! | |
Geom(p) | geometric distribution | f (k) = p^{ }(1-p)^{ k} | |
HG(N,K,n) | hyper-geometric distribution | ||
Bern(p) | Bernoulli distribution |
Combinatorics Symbols:
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
n! | factorial | n! = 1·2·3·…·n | 5! = 1·2·3·4·5 = 120 |
_{n}P_{k} | permutation | _{5}P_{3} = 5! / (5-3)! = 60 | |
_{n}C_{k} | combination | _{5}C_{3} = 5!/[3!(5-3)!]=10 |
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