STAT 462

Geometric Distribution

(1-p)^(y-1)*p

Uniform Distribution (continuous)

1/(theta2-theta1)

Standard Normal distribution

1/Sqrt(2pi)*e^-(z^2/2)

Expected Value & Var -Uniform

E[x]=(theta2+theta1)/2. Var[x]= (theta2-theta1)^2/12

Expected Value & Var -Geometric

E[x]=1/p Var[x]=(1-p)/p^2

Expected Value & var -Beta

E[x]=alpha/(alpha+beta)

Expected Value & Var -Poisson

E[x]=lambda. Var[x]=lambda

Expected Value & Var -Binomial

E[x]=np Var[x]=np(1-p)

Expected value -Hyper Geometric

E[x]=nr/N

Expected Value & Var -Negative Binomial

E[x]=r/p. Var[x]=r(1-p)/p^2

Lambda(alpha)

Integral infinity to zero (y^(alpha-1)e^-y) dy

Negative Binomial Distribution

y-1Cr-1*P^(r-1)*(1-p)^(y-r) Y= attempts. R=Successes

Beta Distribution

y^(alpha-1)(1-y)^(beta-1)/beta(alpha,beta)

Z score

z= x-mean/standard dev

Normal Distribution

[1/omega*Sqrt(2pi)]*e^[-(y-mu)^2/2*omega^2]

Hyper Geometric Distribution

[rCy*N-rCn-y]/NCn N=total items n=sample r= items with characteristic

Gamma, Exponential, and Chi-Square Distributions

[y^(alpha-1)*e^-(y/beta)]/[beta^alpha *lambda(alpha)]

Chi-square distribution

alpha =v/2 beta =2

Exponential Distribution

alpha=1

Poisson Distribution

lambda^y/y! *e^-y

Binomial Distribution

nCy*p(y)^y*(1-p)^(n-y)