how do i find the expection for p(y)=(0.5)^(y+1) for y=0,1,2,3,...
what i did was integrate over 0 to infinity for y(0.5)^(y+1) and i got a negative number instead..
This is a discrete distribution so why are you integrating? You need to evaluate $\displaystyle \sum_{y=0}^{+\infty} \left[y \, \left(\frac{1}{2}\right)^{y+1} \right]$. The calculation is very similar to that of finding the mean of a geometric distribution (which has been done several times in this subforum - use the Search tool to find the threads).