Difference between revisions of "K and k' values"

From Maths
Jump to: navigation, search
(Saving work)
 
m (Adding infinity case for k and k' values)
 
Line 9: Line 9:
 
Given a k'-value, {{M|k'\in\mathbb{N}_{\ge 0} }} then the corresponding probability is:
 
Given a k'-value, {{M|k'\in\mathbb{N}_{\ge 0} }} then the corresponding probability is:
 
* {{MM|p:\eq 1-10^{-k} }}
 
* {{MM|p:\eq 1-10^{-k} }}
===Initial values===
+
===Selected examples===
 
{| class="wikitable" border="1"
 
{| class="wikitable" border="1"
 
|-
 
|-
Line 45: Line 45:
 
| 0.9999
 
| 0.9999
 
| ''9,999 in 10,000''
 
| ''9,999 in 10,000''
 +
|-
 +
! {{M|\vdots}}
 +
| colspan=4 | <center>{{M|\vdots}}</center>
 +
|-
 +
! {{M|\infty}}
 +
| colspan=2 | 0 (impossibility)
 +
| colspan=2 | 1 (certainty)
 
|}
 
|}
 
==Purpose==
 
==Purpose==

Latest revision as of 16:09, 8 February 2018

Stub grade: A**
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Worked on this before bed - needs finishing! Alec (talk) 23:14, 7 February 2018 (UTC)

Definition

Given a probability, [ilmath]p\in[0,1]\subseteq\mathbb{R} [/ilmath] the corresponding values are:

  • [math]k:\eq\frac{-\ln(p) }{\ln(10) } [/math], higher values indicate the event we have the probability for is rarer, eg [ilmath]k\eq 6[/ilmath] is 1 in 1,000,000 (1 million), or [ilmath]p\eq 0.000001[/ilmath]
  • [math]k':\eq\frac{-\ln(1-p)}{\ln(10)} [/math], higher values indicate the event we have the probability for is more common, eg [ilmath]k'\eq 6[/ilmath] is 999,999 in 1,000,000, or [ilmath]p\eq 0.999999[/ilmath]

Given a k-value, [ilmath]k\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:

  • [math]p:\eq 10^{-k} [/math]

Given a k'-value, [ilmath]k'\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:

  • [math]p:\eq 1-10^{-k} [/math]

Selected examples

value, [ilmath]v[/ilmath] [ilmath]v\ \mathbf{k} [/ilmath] (rarity) [ilmath]v\ \mathbf{k}' [/ilmath] (commonality)
(As probability)
0 1 (certainty) 0 (impossibility)
1 0.1 1 in 10 0.9 9 in 10
2 0.01 1 in 100 0.99 99 in 100
3 0.001 1 in 1,000 0.999 999 in 1,000
4 0.0001 1 in 10,000 0.9999 9,999 in 10,000
[ilmath]\vdots[/ilmath]
[ilmath]\vdots[/ilmath]
[ilmath]\infty[/ilmath] 0 (impossibility) 1 (certainty)

Purpose