|
⇤ ← Revision 1 as of 2024-06-14 15:43:35
Size: 981
Comment: Initial commit
|
← Revision 2 as of 2025-04-08 15:20:42 ⇥
Size: 1032
Comment: Typo and reorg
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 3: | Line 3: |
| The '''Bernoulli distribution''' is a discrete propability distribution that gives 1 with probability ''p'' and 0 with probability ''q = 1 - p''. | The '''Bernoulli distribution''' is a discrete probability distribution that gives 1 with probability ''p'' and 0 with probability ''q = 1 - p''. |
| Line 11: | Line 11: |
| == Statistics == | == Description == |
| Line 13: | Line 13: |
| The expected value of a Bernoulli-ditributed variable is ''E[X] = p''. The variance of a Bernoulli-distributed variable is ''Var[X] = p(1 - p) = pq''. |
The distribution is appropriate for modeling any binary outcome. |
| Line 23: | Line 21: |
| == Sampling == | == Statistics == The expected value is ''E[X] = p''. The variance is ''Var[X] = p(1 - p) = pq''. ---- == Usage == === Sampling === |
Bernoulli Distribution
The Bernoulli distribution is a discrete probability distribution that gives 1 with probability p and 0 with probability q = 1 - p.
Description
The distribution is appropriate for modeling any binary outcome.
The sum of repeated and independent Bernoulli-distributed events are described by the binomial distribution.
Statistics
The expected value is E[X] = p.
The variance is Var[X] = p(1 - p) = pq.
Usage
Sampling
If all frame listings have an equal probability of selection, sampling can be implemented like:
scalar p = .2 /* Probability of selection */ set seed 123456789 generate double r = runiform() generate sampled = (r < p)
The expected number of cases sampled is np; the sample size is described by the binomial distribution.