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# 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 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 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 ρX,Y correlation correlation of random variables X and Y ρX,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 = (xmax+xmin)/2 Md sample median half the population is below this value Q1 lower / first quartile 25% of population are below this value Q2 median / second quartile 50% of population are below this value = median of samples Q3 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 zx standard score zx = (x-x) / sx X ~ distribution of X distribution of random variable X X ~ N(0,3) N(μ,σ2) 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 xc-1e-λx / Γ(c), x≥0 χ 2(k) chi-square distribution f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) ) F (k1, k2) F distribution Bin(n,p) binomial distribution f (k) = nCk pk(1-p)n-k Poisson(λ) Poisson distribution f (k) = λke-λ / k! Geom(p) geometric distribution f (k) = p(1-p) k HG(N,K,n) hyper-geometric distribution Bern(p) Bernoulli distribution

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