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• Notes:Geometric probability distribution
  * 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
• Poisson distribution
  |title=Poisson distribution |data1=[[Discrete probability distribution|Discrete]], over {{M|\mathbb{N}_{\ge 0} }}
  8 KB (1,401 words) - 00:52, 20 July 2018
• Alec's c.d.f-sidestepping sampling method
  : See [[generating samples from a distribution]] for and overview of methods used Let {{M|f(x)}} be a [[probability density function|p.d.f]] for which computing {{M|F^{-1}(x)}} is either diff
  3 KB (484 words) - 00:18, 1 October 2017
• Example:Alec's unmarked die experiment
  #* This would model each row as [[Binomial distribution|{{M|\text{Bin} }}]]{{M|\left(\frac{1}{6},45\right)}} #* 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
  5 KB (670 words) - 15:05, 2 October 2017
• Geometric progression
  ** [[Geometric distribution]] - a [[probability distribution]] with ties to geometric sequences. ==Notes==
  3 KB (494 words) - 23:08, 6 October 2017
• Binomial distribution
  |title=Binomial distribution |label1=[[Probability mass function|p.m.f]]
  4 KB (653 words) - 13:11, 22 September 2017
• Geometric distribution
  ...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
• Rectangular distribution
  ==Notes== * [[probability density function]] {{M|f:[a,b]\rightarrow\mathbb{R}_{\ge 0} }} by {{M|f:x\m
  1 KB (204 words) - 05:44, 15 January 2018
• Deriving the exponential distribution from the time between event in a Poisson distribution
  ==Notes== Let {{M|X\sim}}[[Poisson distribution|{{M|\text{Poi}(\lambda)}}]] for some {{M|\lambda\in\mathbb{R}_{>0} }}
  2 KB (298 words) - 03:16, 6 April 2018
• Memoryless property
  ...a point? For the continuous case memoryless {{iff}} it's the [[exponential distribution]] - what about the discrete!}}{{ProbMacro}} ==Notes==
  1 KB (221 words) - 23:02, 11 November 2017
• Exponential distribution/Definition
  * the [[probability density function]], {{M|f:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0} } * the [[cumulative distribution function]], {{M|F:\mathbb{R}_{\ge 0}\rightarrow[0,1]\subseteq\mathbb{R} }},
  1 KB (192 words) - 01:27, 16 March 2018
• The sum of two random variables with Poisson distributions is a Poisson distribution itself
  ...i!}\cdot e^{-r}\frac{r^{k-i} }{(k-i)!} }} - by definition of the [[Poisson distribution]] ...mbda+r)^k}{k!} }} - which the definition of the probability of a [[Poisson distribution|Poisson random variable]] being equal to {{M|k}} whose rate parameter is {{
  3 KB (536 words) - 22:46, 4 November 2017
• Mdm of the Poisson distribution
  {{ProbMacro}}{{Todo|Link with [[Poisson distribution]] page}} Let {{M|X\sim}}[[Poisson distribution|{{M|\text{Poi} }}]]{{M|(\lambda)}} for some {{M|\lambda\in\mathbb{R}_{>0} }
  7 KB (1,308 words) - 00:27, 8 November 2017
• Maximum (random variable)
  {{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
• Poisson race distribution
  Let {{M|X\sim}}[[Poisson distribution|{{M|\text{Poi} }}]]{{M|(\lambda_1)}} and {{M|Y\sim\text{Poi}(\lambda_2)}} b ...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:
  6 KB (1,141 words) - 10:33, 24 December 2018
• Geometric distribution/Infobox
  |title=Geometric Distribution <span style="font-size:0.75em;">''for {{M|p}} the [[probability (event)|probability]] of each trials' success''</span>
  1 KB (226 words) - 15:13, 16 January 2018
• Expectation of the geometric distribution
  ...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}}[ * [[Variance of the geometric distribution]]
  8 KB (1,522 words) - 02:55, 16 January 2018
• Mdm of the Binomial distribution
  ...distribution|{{M|\text{Bin} }}]]{{M|(n,p)}} - so {{M|X}} is a ''[[Binomial distribution|Binomial]]'' [[random variable]] ...tation]] of the [[binomial distribution]], as well as the expression for [[probability]] of {{M|X\eq k}}
  2 KB (282 words) - 01:32, 12 January 2018
• Variance of the geometric distribution
  ...istribution|{{M|\text{Geo} }}]]{{MM|(p) }} - as defined on the [[geometric distribution]] page<ref group="Note">So using ''our'' convention, to say it explicitly</ ...M|p\in(0,1)}} with easy extension (as per ''[[expectation of the geometric distribution]]'') to {{M|p\in(0,1]}}
  3 KB (613 words) - 15:08, 16 January 2018
• Mdm of a discrete distribution lemma
  :* [[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