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Jul. 16th, 2020 05:05 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sigmalephCheck my math?
You flip a coin until it comes up tails. If you get tails immediately, you win $1. If you get one head and then lose on the second round, you win $2. If you get (n-1) heads and lose on the nth round, you win $ 2^(n-1).
Probability of you losing on the first round is 1/2. Probability of you losing on the nth round is 2^-n. Expected value of W (how much you win in USD) is therefore 1/2 + 2*1/4 + ... + 2^(n-1)*2*(^-n) + ... which is a sum of infinitely many terms all equal to 1/2. So the expected value of how much you win is infinite. Is that correct?
(this is not a puzzle or anything, I'm fairly confident I'm right but could be making a mistake)
You flip a coin until it comes up tails. If you get tails immediately, you win $1. If you get one head and then lose on the second round, you win $2. If you get (n-1) heads and lose on the nth round, you win $ 2^(n-1).
Probability of you losing on the first round is 1/2. Probability of you losing on the nth round is 2^-n. Expected value of W (how much you win in USD) is therefore 1/2 + 2*1/4 + ... + 2^(n-1)*2*(^-n) + ... which is a sum of infinitely many terms all equal to 1/2. So the expected value of how much you win is infinite. Is that correct?
(this is not a puzzle or anything, I'm fairly confident I'm right but could be making a mistake)
