Proof of variance for functions of variable

[georg gill]

http://bildr.no/view/1115383

i wonder if anyone could explain the proof for theorem 4.3 i have understood definition 4.3

 

[Karlx]

Hi Georg.
I don't know which is definition 4.1, but it doesn't matter.
If you take definition 4.3 and apply it to the random variable Y=g(X), you'll get it.

 

[georg gill]

http://bildr.no/view/1115856

above is definition 4.1. In the first link that they have forgot to square the variance that appears after the text:

"It follows from Definition 4.3 that.." ?

If they would have done that I would have understood the theorem 4.3 and its proof