# Expectation homework help

1. Apr 12, 2010

Hi I'm going through some presentation material and i cant understand how the following has been derived

$$\sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})]$$

Could someone point me in the right direction on why this makes sense ?

Thanks

2. Apr 13, 2010

### mathman

Re: expectation

It only makes sense if all Kj have the same distribution, although it could hold (by accident) in more general situations.

3. Apr 14, 2010

Re: expectation

ok suppose all $$K_{j}$$ have exactly the same distribution, I still can see why it makes sense. why does the following hold $$\sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})]$$

maybe there is something trivial here that i'm missing but i still cant see it

4. Apr 14, 2010

If all the $K_j$ have the same distribution, so do all of the $\ln (1+K_j)[/tex], and this common distribution is the same as that of [itex] \ln(1+K_1)$.