Question

STATS QUESTION PLEASE!!

http://i289.photobucket.com/albums/ll211/zephyrxX_Y/ScreenShot2013-05-10at75831PM_zpsaba64571.png

don't understand how the first line goes to the second line HELP!!!

Answer 1

I assume we are working with a geometric distribution here?

so, one way of looking at it:

\[\sum_{i=1}^{n}pq^{i-1} = p \sum_{i=1}^{n}q^{i-1}\]

now consider \[\sum_{i=1}^{n} q^{i-1} = 1 + q + q^{2} + ... + q^{n-1}\]

multiply q on both sides:

\[q\sum_{i=1}^{n} q^{i-1} = q + q^{2} + q^3 + ... + q^{n}\]

Subtracking these to expressions:

\[\sum_{i=1}^{n}q^{i-1} - q \sum_{i=1}^{n}q^{i-1} = 1 - q^n\]

so that

\[(1-q)\sum_{i=1}^{n}q^{i-1} = 1 - q^n\]

which yields:

\[\sum_{i=1}^{n}q^{i-1} = {{1-q^n} \over 1- q}\]

so the rest follows.

Answer 2

Thank you veryyyy much!!!!!! =DD