Sums of Independent Random Variables
See also: Convolution and List of convolutions of probability distributionsThe probability density function of the sum of two independent random variables U and V, each of which has a probability density function, is the convolution of their separate density functions:
It is possible to generalize the previous relation to a sum of N independent random variables, with densities U1, …, UN:
This can be derived from a two-way change of variables involving Y=U+V and Z=V, similarly to the example below for the quotient of independent random variables.
Read more about this topic: Probability Density Function
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