Solved – how to calculate the standard deviation of the sum of multiple uniform distribution

Given several independent uniform distributions, such as runif(0,5) and runif(0,50), how to calculate the sd of the sum of the two functions? And in what scenario would one needs to consider the sum of several uniform distributions

To answer the first question, you need the following elements:

1) The variance of a continuously uniformly distributed random variable on the interval $[a,b]$ is $tfrac{1}{12} (b – a)^2$.

2) The variance of the sum of independent (and therefore uncorrelated) random variables is the sum of the variances.

3) The standard deviation is the square root of the variance.

As for the second question, I don't know, how did you come up with it? 🙂

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