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Summary of Discrete Probability Distributions
Description
Examples
p(x) or f(x)
μ = E(x)
Variance
σ
2
Std. Dev.
σ
Binomial
(Discrete)
Experiments involving only two
outcomes. Example: Flipping a coin and
counting number of Heads (X), i.e.
successes
, in a fixed number of trials
(n). On any trial, the probability of
success
is p and probability of
failure
(i.e., obtaining a Tail), q = 1p. When p
= q = 0.5, it's called a symmetric
binomial distribution. NOTE: When n is
large and p is small, binomial
distribution can be approximated by
Poisson distribution with np = Poisson
parameter λ. When n is large, binomial
distribution can also be approximated
by continuous Normal distribution.
n
x
where
q
p
x
n
x
X
P
x
n
x
,..,
2
,
1
,
0
,
)
(
=
=
=

and q = 1 p
np
Note:
Expected number of
failures
= n  E(X)
= n  np
= n(1  p) = nq
npq
npq
Poisson
(Discrete)
A type of probability distribution that is
often useful in describing the number of
times an event occurs in a specific
period of time or in a specific area or
volume. Examples: (i) Number of
customer arrivals per minute at a
supermarket checkout. (ii) Number of
industrial accidents per month at a
manufacturing plant. (iii) Number of
death claims received per day by an
insurance company.
0
,...
3
,
2
,
1
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