Expected value of the log of a uniform distribution

[Gekko]

Homework Statement

How to calculate the expected value of the log of a uniform distribution?

Homework Equations

E[X] where X=ln(U(0,1))

The Attempt at a Solution

integral from 0 to 1 of a.ln(a) da where a = U(0,1)
= -1/4

However I know the answer is -1

 

[8daysAweek]

Why do you integrate over a \cdot ln(a)?

 

[Gekko]

Yes, that's not right I see.

I used this approach instead. To find the first moment of a uniform distribution it is:

1/(b-a) * integral from a to b of x

In this case it is

1/(b-a) * integral from a to b of ln(x)

Is this ok?

This approach calculates the correct value for expected value and variance

 

[vela]

Yup, that's the correct method.