Need help on some Calculus

[wrx07]

My brain is absolutely fried. It's an expected value for continuous random variables type of problem. I would really appreciate the help.

 

[Berlepsch]

First, you expand the (x - m)^2 term and then start to integrate the resulting formula using integration of parts. When you do it right, some terms should cancel each other, leading to the final expression.

 

[Capt Crunch]

First, you expand the (x - m)^2 term and then start to integrate the resulting formula using integration of parts. When you do it right, some terms should cancel each other, leading to the final expression.

You don't need to do this. The integral (in particular the expected value) is a linear operator, so you can take advantage of that. Here's the proof (from wikipedia):

 

[wrx07]

fantastic. thanks a lot! i knew i'd find some math help on a Mac site

 

[Capt Crunch]

fantastic. thanks a lot! i knew i'd find some math help on a Mac site

No problem. Some helpful advice: when in doubt, do the only thing that can be done. In this case, nothing can be done except factor out the (x-mu)^2. Once you do that, there's really nothing you can do except split it into three integrals. That done, you're practically finished. I've found this has helped me for a lot of proofs.