stochastic

r.v.s.: random variable sequence

i.i.d: individual identical distribution

w.p.: with probability

PMF (Probability Mass Function) $P(X=x)$

CDF (Cumulative Distribution Function) $P(X leq x)$

PDF (Probability Density Function) derivate of CDF

PGF (Probability Generating Function) $E(t^X) = sum_{k=0}^{infty} p_k t^k$

MGF (Moment Generating Function) $M(t) = E(e^{tX})$

• Binomial Distribution $Xsim B(n,p)$: number of success in n trails
• HyperGeometric Distribution $Xsim HGeom(w,b,n)$: draw n balls between w white and b black
• Geometric Distribution $Xsim Geom(p)$: number of the Bernoulli trails before success (First Success Distribution)
• Negative Binomial Distribution $Xsim NBin(r,p)$: number of the Bernoulli trails before $r^{th}$ success
• Poisson Distribution $Xsim Pois(lambda)$: number of times an event occurs in an interval of time or space
• Uniform Distribution $Usim Unif(a,b)$: Distribution on the interval $(a,b)$
• Standard Normal Distribution $Xsim N(0,1)$
• Normal Distribution $Xsim N(mu,sigma^2)$
• Beta Distribution $Xsim Beta(a,b)$
• Multinomial Distribution $mathbf{X}sim Mult_k(n,mathbf{p})$