Probability and statistics symbols

Probability and statistics symbols

 

Probability and statistics symbols with Symbol Name , Meaning and definition and also with Example:

Apologies for any confusion. I’ve corrected and reformatted the table according to your request:

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 events A and B occur	P(A ∩ B) = 0.5
P(A ∪ B)	Probability of Events Union	Probability that events A or B occur	P(A ∪ B) = 0.5
P(A	B)	Conditional Probability Function	Probability of event A given event B occurred
f(x)	Probability Density Function (PDF)	Probability distribution function of continuous random variable x	P(a ≤ x ≤ b) = ∫ f(x) dx
F(x)	Cumulative Distribution Function (CDF)	Cumulative probability distribution function of random variable X	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
var(X)	Variance	Variance of random variable X	var(X) = 4
Symbol	Symbol Name	Meaning / Definition	Example
σ²	Variance	Variance of population values	σ² = 4
std(X)	Standard Deviation	Standard deviation of random variable X	std(X) = 2
σX	Standard Deviation	Standard deviation value of random variable X	σX = 2
median	Median	Middle value of random variable x	Median = (2+5+9) / 3 = 5.333
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
ρX,Y	Correlation	Correlation of random variables X and Y	ρX,Y = 0.6
∑	Summation	Sum of all values in the range of a series	∑ xi
∑∑	Double Summation	Double summation	∑∑ xi
Mode	Mode	Value that occurs most frequently in population	Mode = 7
MR	Mid-Range	Mid-range value of a dataset	MR = (xmax + xmin) / 2
Q1	Lower / First Quartile	Value below which 25% of population lies	Q1 = 15
Q2	Median / Second Quartile	Median value of a dataset	Q2 = 25
Q3	Upper / Third Quartile	Value below which 75% of population lies	Q3 = 42
x̄	Sample Mean	Average / arithmetic mean of a sample	x̄ = (2 + 5 + 9) / 3 = 5.333
s²	Sample Variance	Sample variance estimator	s² = 4
s	Sample Standard Deviation	Sample standard deviation estimator	s = 2
z	Standard Score	Standard score of a value x	z = (x – x̄) / s
Symbol	Symbol Name	Meaning / Definition	Example
X ~	Distribution of X	Distribution of random variable X	X ~ N(0,3)
X ~ N(μ,σ²)	Normal Distribution	Gaussian distribution with mean μ and variance σ²	X ~ N(0,3)
X ~ U(a,b)	Uniform Distribution	Equal probability in range [a,b]	X ~ U(0,3)
X ~ exp(λ)	Exponential Distribution	Exponential distribution with rate parameter λ	f(x) = λe^(-λx), x ≥ 0
X ~ gamma(c,λ)	Gamma Distribution	Gamma distribution with shape parameter c and rate parameter λ	f(x) = λ^c x^(c-1) e^(-λx) / Γ(c), x ≥ 0
X ~ χ²(k)	Chi-Square Distribution	Chi-square distribution with k degrees of freedom	f(x) = (x^(k/2-1) e^(-x/2)) / (2^(k/2) Γ(k/2)), x ≥ 0
X ~ F(k₁, k₂)	F Distribution	F distribution with k₁ and k₂ degrees of freedom
X ~ Bin(n,p)	Binomial Distribution	Binomial distribution with parameters n (number of trials) and p (probability of success)	f(k) = nCk p^k (1-p)^(n-k)
X ~ Poisson(λ)	Poisson Distribution	Poisson distribution with parameter λ (average rate of events)	f(k) = λ^k e^(-λ) / k!
X ~ Geom(p)	Geometric Distribution	Geometric distribution with probability of success p	f(k) = p(1-p)^k
X ~ HG(N,K,n)	Hyper-Geometric Distribution	Hyper-geometric distribution with parameters N (population size), K (successes), and n (sample size)
X ~ Bern(p)	Bernoulli Distribution	Bernoulli distribution with parameter p (probability of success)	f(k) = p^k (1-p)^(1-k)

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