Density

Functions F(x)

Probability

Distributions

Discrete

Distributions

Continuous

Distributions

Lognormal

Normal

Beta

Gamma

Chi-square

Exponential

Weibull

Uniform

special case of

Logarithm of these has

a normal distribution

Special case of...

Special case of...

Special case of...

Poisson

Binomial

Bernoulli

Geometric

Negative

Binomial

Probability

Density

Functions f(x)

can be

described by

Probability

Mass

Function p(x)

Cumulative

Distribution

Function F(x)

can be

described by

Sum iid

Bernoullis

to get...

Approximate

for large n

and small p

Number of

trials till

first success

Number of

trials till

r successes

Special case

when r=1

Time between

Poisson process events

Add independent Poissons to

get a new Poisson

Linear combinations of

Normals are normal

Number of observations on a continuous random variable that meet a certain criterion have a Binomial distribution

Central Limit Theorem: Sums and

means of iid random variables have normal distributions for n large.

Sums and means of NORMAL iid variables have NORMAL distributions regardless of

the sample size.

**Conceptual Map of**

Probability Distributions

Probability Distributions

Erlang

Special case of...

Time until rth

Poisson process event

Approximately Normal

for np>=10 and

n(1-p)>=10

Approximately Normal

for large lambda

(say lambda>=10)