Difference between revisions of "Geometric distribution"
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Revision as of 22:24, 29 November 2017
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| Geometric Distribution | |
| X∼Geo(p) for p the probability of each trials' success | |
| X=k means that the first failure occurred on the kth trial, k∈N≥1 | |
| Definition | |
|---|---|
| Defined over | X may take values in N≥0={1,2,…} |
| p.m.f | P[X=k]:=pk−1(1−p) |
| c.d.f / c.m.f[Note 1] | P[X≤k]=1−pk |
| cor: | P[X≥k]=pk−1 |
| Properties | |
| Expectation: | E[X]=1p |
| Variance: | Var(X)=1−pp2 |
Contents
[hide]Notes
during proof of P[X≤k] the result is obtained using a geometric series, however one has to align the sequences (not adjust the sum to start at zero, unless you adjust the Sn formula too!)
Check the variance, I did part the proof, checked the MEI formula book and moved on, I didn't confirm interpretation.
Make a note that my Casio calculator uses 1−p as the parameter, giving P[X=k]:=(1−p)k−1p along with the interpretation that allows 0
Definition
References
Notes
- Jump up ↑ Do we make this distinction for cumulative distributions?
