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Discrete Distributions Name Density Geometric: FX X 1,2, 3,... Pe P Q P X

This document summarizes several discrete probability distributions: 1) It lists several common discrete distributions like geometric, uniform, binomial, Bernoulli, hypergeometric, negative binomial, Poisson, and Poisson approximation to binomial and provides their probability mass functions, expected values, and variances. 2) The distributions covered include geometric, uniform, binomial, Bernoulli, hypergeometric, negative binomial, Poisson, and an approximation of binomial using Poisson. 3) For each distribution, the table provides the probability mass function, expected value/mean, and variance, which are the key metrics to characterize discrete distributions.

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Phạm Đình Quyền
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57 views1 page

Discrete Distributions Name Density Geometric: FX X 1,2, 3,... Pe P Q P X

This document summarizes several discrete probability distributions: 1) It lists several common discrete distributions like geometric, uniform, binomial, Bernoulli, hypergeometric, negative binomial, Poisson, and Poisson approximation to binomial and provides their probability mass functions, expected values, and variances. 2) The distributions covered include geometric, uniform, binomial, Bernoulli, hypergeometric, negative binomial, Poisson, and an approximation of binomial using Poisson. 3) For each distribution, the table provides the probability mass function, expected value/mean, and variance, which are the key metrics to characterize discrete distributions.

Uploaded by

Phạm Đình Quyền
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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Discrete Distributions

Name Density Mx ( t ) E(X) Var ( X )

x = 1,2, 3,... pet 1 q


Geometric f ( x ) = q x 1 p
0 < p<1 1 qet p p2
n 2
n 2
1 x = x1 , x2 , x3 ,..., xn
n

e txi
n

x x xi
2
i

Uniform f ( x) = i i =1
i =1
n n + i =1 i =1
n n
n n

n nx
x = 0,1, 2,..., n n
Binomial f ( x ) = px ( q ) t
( q + pe ) np npq
x 0 < p<1 n +

x = 0,1
Bernoulli f ( x ) = px q1 x q + pet p pq
0 < p<1

r N r
x n x r r N r N n
Hypergeometric f ( x) = max 0, n ( N r) x m in ( n, r) n n
N N N N N 1
n

t r
Negative x 1 x r r x = r, r + 1, r + 2,... ( pe ) r r (1 p)
f ( x) = q p
Binomial r 1 0 < p<1 (1 qe )
t r p p2

e k kx x = 0,1, 2,...
Poisson f ( x) = e
k ( et 1)
k k
x! k > 0 k = s

Poisson Approx. e np ( np)


x goodifn 20 and p .05
f ( x) =
to the Binomial x! very good if n 100 and np 10

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