Variance of continuous random variable

[joselionelvelez]

Study Session 3, Reading 9, Section 3.1 - Continuous Uniform Distribution
I am trying to understand question 2 of Example 7.

1. Estimate the mean and standard deviation of EBITDA/interest. For a continuous uniform random variable, the mean is given by μ = (a + b)/2 and the variance is given by σ2 = (b − a)2/12.

Specifically, I am trying to understand how they deterimined variance. Where did the 12 in the denominator come from???
Thanks!

 

[Harrogath]

I found this as the demonstration: Really accurate, look at the bottom of page 2.
1 / (b - a) is the function of a discrete uniform random variable.
http://nucinkis-lab.cc.ic.ac.uk/HELM/workbooks/workbook_38/38_2_uniform_dist.pdf
Regards

 

[breadmaker]

As Harrogath has pointed out, it’s just a bit of calculus. You only have to know the end result, not the derivation.

 

[joselionelvelez]

This is great! Thanks for the help! Exactly what I was looking for.