View source for Probability Formulas - Rhea

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! style="background: none repeat scroll 0% 0% rgb(228, 188, 126); font-size: 120%;" colspan="2" | 
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="2" | Properties of Probability Functions
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| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring) 
| <math>\,P(A^c) = 1 - P(A)\,</math>
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| align="right" style="padding-right: 1em;" | The intersection of two independent events A and B 
| <math>\,P(A \mbox{ and }B) =  P(A \cap B) = P(A) P(B)\,</math>
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| align="right" style="padding-right: 1em;" | The union of two events A and B (i.e. either A or B occurring) 
| <math>\,P(A \mbox{ or } B) = P(A) + P(B) - P(A \mbox{ and } B)\,</math>
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| align="right" style="padding-right: 1em;" | The union of two mutually exclusive events A and B 
| <math>\,P(A \mbox{ or } B) =  P(A \cup B)= P(A) + P(B)\,</math>
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| align="right" style="padding-right: 1em;" | Event A occurs given that event B has occurred 
| <math>\,P(A \mid B) = \frac{P(A \cap B)}{P(B)}\,</math>
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| align="right" style="padding-right: 1em;" | Total Probability Law 
| <math>\,P(B) = P(B|A_1)P(A_1) + \dots + P(B|A_n)P(A_n)\,</math> 
 <math> \mbox{ where } \{A_1,\dots,A_n\} \mbox{ is a partition of sample space } S, B \mbox{ is an event }.</math>

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| align="right" style="padding-right: 1em;" | Bayes Theorem 
| <math>\,P(A_j|B) = \frac{P(B|A_j)P(A_j)}{\sum_{i=1}^{n}P(B|A_i)P(A_i)},\ \{A_i\} \mbox{ and } B \mbox{ are as above }.</math>
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="4" | Expectation and Variance of Random Variables
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| align="right" style="padding-right: 1em;" | Binomial random variable with parameters n and p 
| <math>\,E[X] = np,\ \ Var(X) = np(1-p)\,</math>
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| align="right" style="padding-right: 1em;" | Poisson random variable with parameter <math>\lambda</math>
| <math>\,E[X] = \lambda,\ \ Var(X) = \lambda\,</math> 
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| align="right" style="padding-right: 1em;" | Geometric random variable with parameter p
| <math>\,E[X] = \frac{1}{p},\ \ Var(X) = \frac{1-p}{p^2}\,</math> 
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| align="right" style="padding-right: 1em;" | Uniform random variable over (a,b)
| <math>\,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\,</math> 
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| align="right" style="padding-right: 1em;" | Gaussian random variable with parameter <math>\mu \mbox{ and } \sigma^2</math>
| <math>\,E[X] = \mu,\ \ Var(X) = \sigma^2\,</math> 
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