Conduct Web experiments using PHP, Part 2

By Paul Meagher
2005-03-18

Discrete probability distributions

In CDA, three discrete probability distributions are commonly used in sampling models. Table 3 lists probability distributions along with other basic information about them.

Table 3. Commonly used discrete probability distributions

Distribution	Parameters	Probability Density Function	Mean	Variance
Binomial	n, p	P(x \| n, p) = n! / ((n-x)! x!) pⁿ (1 - p)^n-x	np	np(1 - p)
Poisson		P(x \| ) = ( ^x e^-λ ) / x!
Multinomial	n, p₁, .., p_n	P(x₁,.., x_n \| n, p₁,.., p_n) = ( n! / x₁! .. x_n! ) p₁^x₁ .. p_n^x_n	np_i	np_i(1 - p_i)

Tutorial Pages:
» Categorical data analysis
» 2x2 contingency tables
» Sampling model
» Discrete probability distributions
» Binomial sampling model
» Poisson sampling model
» Envisioning your results
» Eliciting your prior distribution
» Model fitting with chi-square
» Null effects model
» Independence model
» Prior model
» DOE explorer
» Explorer output
» Conclusions
» Resources

First published by IBM developerWorks

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