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Probability Distributions Mind Map

Math 362
by

Eric Nordmoe

on 26 May 2011

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Transcript of Probability Distributions Mind Map

Cumulative
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

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)
Full transcript