Bernoulli Distribution
A Distribution given by
 |  |  | (1) |
|  | (2) |
The distribution of heads and tails in Coin Tossing is a Bernoulli distribution with
. TheGenerating Function of the Bernoulli distribution is | (3) |
 | |  | (4) |
 | |  | (5) |
 | | | (6) |
 | |  | (7) |
and the Moments about 0 are
 | |  | (8) |
 | |  | (9) |
 | |  | (10) |
The Moments about the Mean are
 | |  | (11) |
 | |  | |
|  | (12) | |
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|  | ||
|  | (13) |
The Mean, Variance, Skewness, and Kurtosis are then
 | |  | (14) |
 | |  | (15) |
 | |  | |
|  | (16) | |
 | |  | |
|  | (17) |
To find an estimator for a population mean,
 | |  | |
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|  | (18) |
so
is an Unbiased Estimator for 
. The probability of 
successes in 
trials is then | (19) |
 | (20) |
- Bordism Group
- Borel-Cantelli Lemma
- Borel Determinacy Theorem
- Borel Measure
- Borel Probability Measure
- Borel Set
- Borel's Expansion
- Borel Sigma Algebra
- Borel Space
- Borromean Rings
- Borrow
- Borsuk's Conjecture
- Borwein Conjectures
- Bouligand Dimension
- Bound
- Boundary
- Boundary Conditions
- Boundary Map
- Boundary Point
- Boundary Set
- Boundary Value Problem
- Bounded
- Bounded Variation
- Bound Variable
- Bourget Function