What is the variance of a continuous uniform distribution

CFA Level I
#1

Specific question, I know. Mean: (a+b)/2 That’s easy to understand. Variance: (b-a)^2 / 12 This is in the cfa text 1, page 388. Why do we divide by 12?!?

#2

That’s beyond what we need to know for the exam, but it is a good question.

#3

Var(X) = EX^2 - (E(X))^2 E(X) = (a + b)/2 as above E(X^2) = integral from a to b x^2 * (1/(b-a)) then do the algebra…

#4

joey, do the calculus please.

#5

integral from a to b x^2 * (1/(b-a)) = (b^3/3 - a^3/3) * (1/(b-a)) So, uh, Var(X) = (b^3/3 - a^3/3) * (1/(b-a)) - (a+b)^2/4 = [b^2 + ab + a^2]/3 - [a^2+2ab+b^2]/4 = [4b^2 + 4ab + 4a^2 - 3a^2 - 6ab - 3b^2]/12 = [b^2 - 2ab -a^2]/12 = (b-a)^2/12 Edit: Women really dig algebra like that.

#6

That’s cool.