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- * [[Discrete probability measure]] ==Notes==6 KB (941 words) - 14:39, 16 August 2016
- ...agram to remember. I remember ''ring'' easily (it's what you'd need to "do probability" on, unions and set-subtractions, and the empty set (required to have subtr ==Other Notes==3 KB (449 words) - 20:06, 19 August 2016
- | {{M|\backslash}}-closed<ref name="PTACC">Probability Theory - A comprehensive course - Second Edition - Achim Klenke</ref> ==Notes==2 KB (360 words) - 20:43, 15 June 2015
- ...al{A} }} is a system of subsets of {{M|\Omega}} such that<ref name="PTACC">Probability Theory - A comprehensive course - Achim Klenke</ref>: ==Notes==1 KB (165 words) - 20:50, 15 June 2015
- ==Notes for further claims== ==Notes==3 KB (490 words) - 11:38, 21 August 2016
- See [[Notes:Just what is in a generated sigma-algebra|Just what is in a generated {{Sig ...the [[Power set|power set]] of {{M|\Omega}}) there exists<ref name="PTACC">Probability Theory - A Comprehensive Course - Second Edition - Achim Klenke</ref> a sma2 KB (286 words) - 22:02, 17 March 2016
- '''Note: '''a Dynkin system is also called a "{{M|d}}-system"<ref>Probability and Stochastics - Erhan Cinlar</ref> and the page [[d-system]] just redirec ==Notes==1 KB (184 words) - 01:54, 19 March 2016
- ...\mathcal{D}\subseteq\mathcal{P}(X)}} is a ''Dynkin system''<ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref> on {{M|X}} if: ==Notes==719 B (120 words) - 23:22, 2 August 2015
- ...\mathcal{F}=\sigma(\mathcal{G})}}</ref> we have{{rMIAMRLS}}<ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref>: ==Notes==2 KB (328 words) - 13:23, 18 March 2016
- ! Numerical function on {{M|A}}<ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref> ==Notes==1 KB (165 words) - 02:07, 3 August 2015
- ...ef><ref group="Note">Product sometimes means 'intersection' according to ''Probability and Stochastics - Erhan Cinlar'' - this is Dynkin's own naming system</ref> ==Notes==960 B (158 words) - 15:43, 28 August 2015
- : Also; in probability I can observe an event ''not'' happening, this suggests I might actually wa ==Notes (yes on a notes page)==5 KB (771 words) - 03:06, 21 March 2016
- * Let {{M|X\sim\text{Geometrically}(p)}} where {{M|p}} is the [[probability]] of an event happening. ** {{M|1=\mathbb{P}\left[X=n\right]=(1-p)^{n-1}p}} - that is the probability of an event not happing {{M|n-1}} times, then happening on the {{M|n^\text{968 B (171 words) - 19:37, 2 June 2016
- ! [[Ring of sets|Ring]]<ref name="PTACC">Probability Theory - A comprehensive course - second edition - Achim Klenke</ref>{{rMTH ==Notes==4 KB (573 words) - 20:00, 19 August 2016
- {{Stub page|grade=A**|msg=This page is a stub and just notes, it needs to be done formally and fleshed out [[User:Alec|Alec]] ([[User ta ...l that {{MM|\E{X}:\eq\int^\infty_0 xf(x)\mathrm{d}x}} for {{M|f(x)}} the [[probability density function]].1 KB (246 words) - 21:29, 11 January 2018
- |data1=[[Discrete probability distribution|Discrete]], over {{M|\mathbb{N}_{\ge 0} }} |label2=[[Probability mass function|p.m.f]]8 KB (1,401 words) - 00:52, 20 July 2018
- Define a [[probability space]], {{M|(S,\Omega,\mathbb{P})}} as follows: ==PAGE NOTES==7 KB (1,100 words) - 19:36, 13 September 2017
- Let {{M|f(x)}} be a [[probability density function|p.d.f]] for which computing {{M|F^{-1}(x)}} is either diff ...{h(x)}{\int_Ah(t)\mathrm{d}t} }} - note that this makes {{M|g}} itself a [[probability density function|p.d.f]]3 KB (484 words) - 00:18, 1 October 2017
- #* For example, there were 38 values of six, if random we'd expect the probability of any individual 6 value being recorded in any particular digit as 1/5 ==Notes==5 KB (670 words) - 15:05, 2 October 2017
- ** [[Geometric distribution]] - a [[probability distribution]] with ties to geometric sequences. ==Notes==3 KB (494 words) - 23:08, 6 October 2017
- : {{Warning|This page is for ''my'' notes on work I haven't done for 5 years, don't rely on it}} - this is mainly for ...times called a '''type-II error''' or a '''type-B error''' - we denote the probability of such error as {{M|\epsilon_b}}2 KB (264 words) - 15:13, 3 October 2017
- |label1=[[Probability mass function|p.m.f]] ...the [[probability of]] a head on a single flip) we can just multiply that probability by 3.4 KB (653 words) - 13:11, 22 September 2017
- ...ith {{M|X_i\sim}}[[Borv|{{M|\text{Borv} }}]]{{M|(p)}}, so {{M|p}} is the [[probability]] of any particular trial being a "success". The geometric distribution models the probability that the ''first'' success occurs on the {{M|k^\text{th} }} trial, for {{M|3 KB (557 words) - 15:14, 16 January 2018
- Let {{M|(S,\Omega,\mathbb{P})}} be a [[probability space]], let {{M|(U_i)_{i\eq 1}^n\subseteq\Omega}} be a finite collection o ==Notes==2 KB (398 words) - 01:50, 7 October 2017
- ...})}} be a [[probability space]] and let {{M|A,B\in\Omega}} be {{link|event|probability|s}}. We say "{{M|A}} and {{M|B}} are ''statistically independent'' if: * The probability of {{M|A}} is the same as the probability of {{M|A}} given {{M|B}} has occurred, and,2 KB (372 words) - 13:47, 17 October 2017
- ==Notes== * [[probability density function]] {{M|f:[a,b]\rightarrow\mathbb{R}_{\ge 0} }} by {{M|f:x\m1 KB (204 words) - 05:44, 15 January 2018
- ==Notes== ==Notes==2 KB (298 words) - 03:16, 6 April 2018
- ==Notes== {{Definition|Statistics|Probability|Elementary Probability}}1 KB (221 words) - 23:02, 11 November 2017
- ==Notes== {{Definition|Elementary Probability|Statistics|Probability}}191 B (17 words) - 23:06, 11 November 2017
- * the [[probability density function]], {{M|f:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0} } ==Notes==1 KB (192 words) - 01:27, 16 March 2018
- ...e^{-(\lambda+r)} \frac{(\lambda+r)^k}{k!} }} - which the definition of the probability of a [[Poisson distribution|Poisson random variable]] being equal to {{M|k} ==Notes==3 KB (536 words) - 22:46, 4 November 2017
- ==Notes== {{Theorem Of|Probability|Statistics|Elementary Probability}}7 KB (1,308 words) - 00:27, 8 November 2017
- {{Stub page|This page is currently little more than notes, beware. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 18:56, 26 November 20 ==Definition notes==4 KB (791 words) - 18:57, 26 November 2017
- ...M|\sum_{i\in\mathbb{N}_0}a_i}} means {{M|\sum^\infty_{i\eq 0}a_i}} - see [[Notes:Infinity notation]]</ref>, which may be written: ====NOTES for {{M|k<0}}====6 KB (1,141 words) - 10:33, 24 December 2018
- ...subset of the natural numbers. There are some options in this case, see [[Notes:Median of an ordered unit type sample]]. ==Notes==3 KB (526 words) - 07:25, 11 December 2017
- <span style="font-size:0.75em;">''for {{M|p}} the [[probability (event)|probability]] of each trials' success''</span> |label2=[[probability mass function|p.m.f]]1 KB (226 words) - 15:13, 16 January 2018
- ...Geometric distribution|{{M|\text{Geo} }}]]{{M|(p)}} where {{M|p}} is the [[probability]] of any trial being a success, and each trial is {{iid}} as {{M|X_i\sim}}[ ==Notes==8 KB (1,522 words) - 02:55, 16 January 2018
- ::: {{Green highlight|This was solved/worked out, see: [[Probability of i.i.d random variables being in an order and not greater than something] ==Notes==2 KB (477 words) - 03:44, 12 December 2017
- ...tation]] of the [[binomial distribution]], as well as the expression for [[probability]] of {{M|X\eq k}} ==Notes==2 KB (282 words) - 01:32, 12 January 2018
- ==Notes== {{Theorem Of|Probability|Statistics|Elementary Probability}}3 KB (613 words) - 15:08, 16 January 2018
- :* [[Notes:Mdm of a discrete distribution lemma]] :* [[Notes:Mdm of a discrete distribution lemma - round 2]]{{ProbMacros}}2 KB (419 words) - 17:53, 24 January 2018
- =Original notes= ==Page notes==6 KB (1,125 words) - 01:31, 22 January 2018
- ==Notes== {{Notes|Statistics|Probability|Elementary Probability}}3 KB (508 words) - 21:01, 24 January 2018
- ==Notes== ...th the property failing the test being an ''impossibility'' we require the probability of the test being positive ''given'' the subject has the property is comple4 KB (859 words) - 09:17, 29 January 2018
- This actually might just be the definition of joint probability applied to tests.... ...S,\Omega,\mathbb{P})}}<ref group="Note" name="CriticalSidestep"/> be the [[probability space]] we take subjects from (so each subject takes a value in {{M|S}}, so2 KB (404 words) - 00:29, 17 February 2018
- If an event will never occur (see: [[event has a probability of zero]], or {{XXX|Dare I say: }} is impossible {{XXX|Check terminology}}) ** We can replace the word "rarity" with "probability" - but in this case the unit "''kays''" '''''must''''' be given4 KB (573 words) - 19:42, 14 June 2018
- ...ig) }} - which is just a standard composition {{XXX|Is this [[law of total probability]]?}} ==Notes==3 KB (509 words) - 00:41, 20 July 2018
- ==Notes== {{Definition|Analysis|Real Analysis|Measure Theory|Probability|Statistics|Order Theory}}<!-- TODO XXX Check these categories match with "M3 KB (473 words) - 07:53, 28 July 2018
