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RV Distributions DISCRETE
PMFs, CDFs, Expected Values, and Variances of common discrete random varibles
10
Mathematics
Undergraduate 2
11/12/2012
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Term
Bernoulli Notation and PMF
 Definition

X~Bern(p)

p(1) = p and p(0) = 1 − p
Term
Binomial Notation and PMF
 Definition

X~Bin(n,p)

p(k) =( nk)pk(1 − p)n−k

for k = 0, 1, . . . , n
Term
Poisson Notation and PMF
 Definition

X~Pois(λ)

pmf= (λke-λ)/(k!)
Term
Negative Binomial Notation and PMF
 Definition

X~NegBin(r,p)

pmf= (k-1r-1)pr(1-p)k-r

for k>=r
Term
Bernoulli Expected Value and Variance
 Definition

E(X)=p

V(X)=p(1-p)
Term
Binomial Expected Value and Variance
 Definition

E(X)=np

V(X)=np(1-p)
Term
Poisson Expected Value and Variance
 Definition
E(X)=V(X)=λ
Term
Negative Binomial Expected Value and Variance
 Definition

E(X)=r/p

V(X)=r(1-p)/p2
Term

Geometric Notation and PMF

 Definition

X~Geom(p)

pmf= pk(1-p)k-1

for k= 0,1,2...
Term
Geometric Expected Value and Variance
 Definition

E(X)=1/p

V(X)=(1-p)/p2
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