Probability distribution of a sum of uniform random variables

$\begingroup$

Given a random variable $$X = \sum_i^n x_i,$$where $x_i \in (a_i,b_i)$ are independent uniform random variables, how does one find the probability distribution of $X$?

$\endgroup$ 1

2 Answers

$\begingroup$

The sum of $n$ iid random variables with (continuous) uniform distribution on $[0,1]$ has distribution called the Irwin-Hall distribution. Some details about the distribution, including the cdf, can be found at the above link. One can then get corresponding information for uniforms on $]a,b]$ by linear transformation.

$\endgroup$ 9 $\begingroup$

The PDF of $X$ is given by the convolution of the PDFs of the variables $x_i$.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy