Title: Memoryless -- from Wolfram MathWorld
Open Graph Title: Memoryless -- from Wolfram MathWorld
X Title: Memoryless -- from Wolfram MathWorld
Description: A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) The exponential distribution satisfies P(x>t) = e^(-lambdat) (4) P(x>s+t) = e^(-lambda(s+t)), (5) and therefore P(x>s+t) = P(x>s)P(x>t) (6) = e^(-lambdas)e^(-lambdat) (7) = e^(-lambda(s+t)), (8) is the only memoryless random distribution. If s and t are...
Open Graph Description: A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) The exponential distribution satisfies P(x>t) = e^(-lambdat) (4) P(x>s+t) = e^(-lambda(s+t)), (5) and therefore P(x>s+t) = P(x>s)P(x>t) (6) = e^(-lambdas)e^(-lambdat) (7) = e^(-lambda(s+t)), (8) is the only memoryless random distribution. If s and t are...
X Description: A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) The exponential distribution satisfies P(x>t) = e^(-lambdat) (4) P(x>s+t) = e^(-lambda(s+t)), (5) and therefore P(x>s+t) = P(x>s)P(x>t) (6) = e^(-lambdas)e^(-lambdat) (7) = e^(-lambda(s+t)), (8) is the only memoryless random distribution. If s and t are...
Opengraph URL: https://mathworld.wolfram.com/Memoryless.html
Domain: mathworld.wolfram.com
| DC.Title | Memoryless |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) The exponential distribution satisfies P(x>t) = e^(-lambdat) (4) P(x>s+t) = e^(-lambda(s+t)), (5) and therefore P(x>s+t) = P(x>s)P(x>t) (6) = e^(-lambdas)e^(-lambdat) (7) = e^(-lambda(s+t)), (8) is the only memoryless random distribution. If s and t are... |
| DC.Date.Modified | 2006-03-22 |
| DC.Subject | 62E |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/Memoryless.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2006-03-22 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Memoryless.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Memoryless.png |
| None | ie=edge |
Links:
Viewport: width=device-width, initial-scale=1