Variance of continuous random variable

joselionelvelez · September 28, 2015, 7:42pm

Study Session 3, Reading 9, Section 3.1 - Continuous Uniform Distribution

I am trying to understand question 2 of Example 7.

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 · September 28, 2015, 9:16pm

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.

Regards

breadmaker · September 28, 2015, 10:19pm

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

joselionelvelez · September 29, 2015, 1:41pm

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