1. Useful Discrete Random Variables
Duncan MacFarlane
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

2. PMF of Geometric Random Variables
P(x) = px(1-p)(x-1)
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

3. CDF of the Geometric Distribution
P(x) = px(1-p)(x-1)
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

4. PMF of Binomial Random Variable, n=10
(nx)px(1-p) (n-x)
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

5. CDF of the Binomial Distribution
(nx)px(1-p) (n-x)
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

6. Poisson Random Variable -- arrival statistics
P(x) = αxexp(-α)/x!
α=T
=(ave arriv/sec)(observ time)
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

7. CDF of the Poisson Distribution
αxexp(-α)/x!
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane

8. The Erik Jonsson School of Engineering and Computer Science
Summary of Results
Distribution
Formula
E[X]
Var[X]
Bernoulli
(1-p) if x=0
Or p if x=1 p
p(1-p)
geometric
px(1-p)(x-1)
1/p
(1-p)/p2
binomial
(nx)px(1-p) (n-x) np
np(1-p)
Pascal
(x-1k-1)pk(1-p) (x-k)
k/p
p(1-p)/ p2
Poisson
αxexp(-α)/x! α
discrete uniform
1/(l-k-1) if x=k…l
Or otherwise
(k+l)/2
(l-k)(l-k+2)/12
The Erik Jonsson School of Engineering and Computer Science
© Duncan L. MacFarlane