Convolution
Topic of Functions of random variables and limit theorems, part of Probability
Convolution
| Type | Topic |
| Taught in | Functions of random variables and limit theorems |
| Part | Probability |
The distribution of a sum of independent random variables. For densities, f_{X+Y}(z)=\int f_X(x)f_Y(z-x)\,dx; for mass functions the integral is a sum. Generating functions turn a convolution into a product.
In Functions of random variables and limit theorems
The sum of two independent continuous variables has density equal to the convolution
f_{X+Y}(z)=\int_{-\infty}^{\infty} f_X(x)\,f_Y(z-x)\,\,\mathrm{d} x.
Used in
See also
Independent random variables · Discrete distribution · Distribution of a function or a sum · Transformation rule · Multivariate normal distribution · Affine images of normal vectors · Normal linear model · Law of large numbers