Expected value of the log of a uniform distribution

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Homework Help Overview

The discussion revolves around calculating the expected value of the logarithm of a uniform distribution, specifically focusing on the uniform distribution defined on the interval (0, 1).

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to calculate the expected value using an integral approach but questions the correctness of their result. Other participants discuss integrating ln(x) over the uniform distribution and explore the method for finding the first moment.

Discussion Status

Participants are exploring different methods to calculate the expected value, with some guidance provided on the correct approach. There is acknowledgment of errors in initial attempts, and a method is suggested that aligns with standard practices for calculating moments of distributions.

Contextual Notes

There is a mention of the expected value and variance in the context of uniform distributions, indicating that the discussion is framed within the constraints of typical homework problems.

Gekko
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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
 
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Why do you integrate over a \cdot ln(a)?
 
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
 
Last edited:
Yup, that's the correct method.
 

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