## Probability and statistics symbols

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= 4^{2 } |

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)/2_{min} | |

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) = (1_{n}C_{k} p^{k}-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 |