Title: Normal Difference Distribution -- from Wolfram MathWorld
Open Graph Title: Normal Difference Distribution -- from Wolfram MathWorld
X Title: Normal Difference Distribution -- from Wolfram MathWorld
Description: Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is given by P_(X-Y)(u) = int_(-infty)^inftyint_(-infty)^infty(e^(-x^2/(2sigma_x^2)))/(sigma_xsqrt(2pi))(e^(-y^2/(2sigma_y^2)))/(sigma_ysqrt(2pi))delta((x-y)-u)dxdy (1) = (e^(-[u-(mu_x-mu_y)]^2/[2(sigma_x^2+sigma_y^2)]))/(sqrt(2pi(sigma_x^2+sigma_y^2))), (2) where delta(x) is a delta function, which is another normal...
Open Graph Description: Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is given by P_(X-Y)(u) = int_(-infty)^inftyint_(-infty)^infty(e^(-x^2/(2sigma_x^2)))/(sigma_xsqrt(2pi))(e^(-y^2/(2sigma_y^2)))/(sigma_ysqrt(2pi))delta((x-y)-u)dxdy (1) = (e^(-[u-(mu_x-mu_y)]^2/[2(sigma_x^2+sigma_y^2)]))/(sqrt(2pi(sigma_x^2+sigma_y^2))), (2) where delta(x) is a delta function, which is another normal...
X Description: Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is given by P_(X-Y)(u) = int_(-infty)^inftyint_(-infty)^infty(e^(-x^2/(2sigma_x^2)))/(sigma_xsqrt(2pi))(e^(-y^2/(2sigma_y^2)))/(sigma_ysqrt(2pi))delta((x-y)-u)dxdy (1) = (e^(-[u-(mu_x-mu_y)]^2/[2(sigma_x^2+sigma_y^2)]))/(sqrt(2pi(sigma_x^2+sigma_y^2))), (2) where delta(x) is a delta function, which is another normal...
Opengraph URL: https://mathworld.wolfram.com/NormalDifferenceDistribution.html
Domain: mathworld.wolfram.com
| DC.Title | Normal Difference Distribution |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is given by P_(X-Y)(u) = int_(-infty)^inftyint_(-infty)^infty(e^(-x^2/(2sigma_x^2)))/(sigma_xsqrt(2pi))(e^(-y^2/(2sigma_y^2)))/(sigma_ysqrt(2pi))delta((x-y)-u)dxdy (1) = (e^(-[u-(mu_x-mu_y)]^2/[2(sigma_x^2+sigma_y^2)]))/(sqrt(2pi(sigma_x^2+sigma_y^2))), (2) where delta(x) is a delta function, which is another normal... |
| DC.Date.Created | 2003-07-03 |
| DC.Date.Modified | 2003-11-03 |
| 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/NormalDifferenceDistribution.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2003-11-03 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_NormalDifferenceDistribution.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_NormalDifferenceDistribution.png |
| None | ie=edge |
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