Difference between revisions of "Geometric distribution/Infobox"
From Maths
(Pulling infobox out) |
m (Adding variance) |
||
| Line 22: | Line 22: | ||
|data10={{MM|\mathbb{E}[X]\eq\frac{1}{p} }}<ref>See ''[[Expectation of the geometric distribution]]''</ref> | |data10={{MM|\mathbb{E}[X]\eq\frac{1}{p} }}<ref>See ''[[Expectation of the geometric distribution]]''</ref> | ||
|label11=[[Variance]]: | |label11=[[Variance]]: | ||
| − | |data11={{Nowrap|{{ | + | |data11={{Nowrap|{{MM|\text{Var}(X)\eq\frac{1-p}{p^2} }}<ref>See ''[[Variance of the geometric distribution]]''</ref>}} |
}}<noinclude> | }}<noinclude> | ||
: '''PAGE FOR TRANSCLUSION, YOU PROBABLY WANT [[Geometric distribution|''GEOMETRIC DISTRIBUTION'']]''' | : '''PAGE FOR TRANSCLUSION, YOU PROBABLY WANT [[Geometric distribution|''GEOMETRIC DISTRIBUTION'']]''' | ||
Latest revision as of 15:13, 16 January 2018
| Geometric Distribution | |
| [ilmath]X\sim\text{Geo}(p)[/ilmath] for [ilmath]p[/ilmath] the probability of each trials' success | |
| [ilmath]X\eq k[/ilmath] means that the first success occurred on the [ilmath]k^\text{th} [/ilmath] trial, [ilmath]k\in\mathbb{N}_{\ge 1} [/ilmath] | |
| Definition | |
|---|---|
| Defined over | [ilmath]X[/ilmath] may take values in [ilmath]\mathbb{N}_{\ge 1}\eq\{1,2,\ldots\} [/ilmath] |
| p.m.f | [ilmath]\mathbb{P}[X\eq k]:\eq (1-p)^{k-1}p[/ilmath] |
| c.d.f / c.m.f[Note 1] | [ilmath]\mathbb{P}[X\le k]\eq 1-(1-p)^k[/ilmath] |
| cor: | [ilmath]\mathbb{P}[X\ge k]\eq (1-p)^{k-1} [/ilmath] |
| Properties | |
| Expectation: | [math]\mathbb{E}[X]\eq\frac{1}{p} [/math][1] |
| Variance: | [math]\text{Var}(X)\eq\frac{1-p}{p^2} [/math][2] |
- PAGE FOR TRANSCLUSION, YOU PROBABLY WANT GEOMETRIC DISTRIBUTION
Notes
- ↑ Do we make this distinction for cumulative distributions?
