Probability is the chance that something will happen – how likely it is that some event will happen. Statistics is the study of data: how to collect, summarize and present it. Probability and statistics are separate but two related academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together.
List of Probability and Statistics Symbols
You can explore Probability and Statistics Symbols, name meanings and examples below-
Symbol |
Symbol Name |
Meaning / definition |
Example |
| P(A ∩ B) | probability of events intersection | probability that of events A and B | P(A∩B) = 0.5 |
| P(A) | probability function | probability of event A | P(A) = 0.5 |
| P(A | B) | conditional probability function | probability of event A given event B occurred | P(A | B) = 0.3 |
| P(A ∪ B) | probability of events union | probability that of events A or B | P(A∪B) = 0.5 |
| F(x) | cumulative distribution function (cdf) | F(x) = P(X ≤ x) | |
| f (x) | probability density function (pdf) | P(a ≤ x ≤ b) = ∫ f (x) dx | |
| E(X) | expectation value | expected value of random variable X | E(X) = 10 |
| μ | population mean | mean of population values | μ = 10 |
| var(X) | variance | variance of random variable X | var(X) = 4 |
| E(X | Y) | conditional expectation | expected value of random variable X given Y | E(X | Y=2) = 5 |
| std(X) | standard deviation | standard deviation of random variable X | std(X) = 2 |
| σ2 | variance | variance of population values | σ2 = 4 |
\(\begin{array}{l}\widetilde{x}\end{array} \) |
median | middle value of random variable x | \(\begin{array}{l}\widetilde{x}= 5\end{array} \) |
| σX | standard deviation | standard deviation value of random variable X | σX = 2 |
| corr(X,Y) | correlation | correlation of random variables X and Y | corr(X,Y) = 0.6 |
| cov(X,Y) | covariance | covariance of random variables X and Y | cov(X,Y) = 4 |
| ρX,Y | correlation | correlation of random variables X and Y | ρX,Y = 0.6 |
| Mo | mode | value that occurs most frequently in population | |
| Md | sample median | half the population is below this value | |
| MR | mid-range | MR = (xmax+xmin)/2 | |
| Q2 | median / second quartile | 50% of population are below this value = median of samples | |
| Q1 | lower / first quartile | 25% of population are below this value | |
| x | sample mean | average / arithmetic mean | x = (2+5+9) / 3 = 5.333 |
| Q3 | upper / third quartile | 75% of population are below this value | |
| s | sample standard deviation | population samples standard deviation estimator | s = 2 |
| s 2 | sample variance | population samples variance estimator | s 2 = 4 |
| X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) |
| zx | standard score | zx = (x–x) / sx | |
| U(a,b) | uniform distribution | equal probability in range a,b | X ~ U(0,3) |
| N(μ,σ2) | normal distribution | gaussian distribution | X ~ N(0,3) |
| gamma(c, λ) | gamma distribution | f (x) = λ c xc-1e-λx / Γ(c), x≥0 | |
| exp(λ) | exponential distribution | f (x) = λe–λx , x≥0 | |
| F (k1, k2) | F distribution | ||
| Bin(n,p) | binomial distribution | f (k) = nCk pk(1-p)n-k | |
| χ 2(k) | chi-square distribution | f (x) = xk/2-1e–x/2 / ( 2k/2 Γ(k/2) ) | |
| Geom(p) | geometric distribution | f (k) = p (1-p) k | |
| Poisson(λ) | Poisson distribution | f (k) = λke–λ / k! | |
| Bern(p) | Bernoulli distribution | ||
| HG(N,K,n) | hypergeometric distribution |
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