# Homework Help: Statistics expectation of discrete variable.

1. May 13, 2013

### peripatein

Hi,

1. The problem statement, all variables and given/known data

How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges?
Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4?

2. Relevant equations

3. The attempt at a solution
I am really not sure how to analyse that series. I have managed to determine, through the ratio test, that it indeed converges, but I am not sure how to break it down so that it could be easily determined to what number it converges. I'd truly appreciate some assistance.

2. May 13, 2013

### tiny-tim

hi peripatein!
calculus?
i don't understand

what is Y ?

3. May 13, 2013

### peripatein

Y is just a discrete variable for which the probability is P(Y) = 1/2m-1. But how is E(Y) 2 (based on the answers in the book)?! Why is it not 4?
And I realise calculus would render the evaluation of Ʃ(m=1 to ∞) m/2m-1 possible, yet I am not sure how to break it down. Could you help?

4. May 13, 2013

### tiny-tim

hi peripatein!
start by writing f(x) = ∑ mx-(m-1)
do you mean P(Y=m) ?

5. May 14, 2013

### haruspex

Do those probabilities add up to 1?