If a dice is thrown until we get an even number, what is the expected no. of throws?
Would this be the same as finding the expected value
There may be a way to solve without infinite sum as well.
I intentionally omitted the sum, so that you can work it out on your own, or say where you got stuck..
Edit: I was able to evaluate the sum by calling the sum L and then computing L + 2L which can be manipulated to 2 + 2L .... but it seems a bit messy.
We get the sum E(X) = 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ...
Above I mention a method of evaluating the sum, after which we will get E(X) = 2. Like I wrote above, the way I found seems kind of messy, but maybe that's a standard way, don't really know. If you want me to show you I can.