4
$\begingroup$

This should be known as "gambler's ruin". In a game, at each step, you can win 1\$ or lose 1\$. Let $Z_i$ be a variable that can assume as values 1 or -1. Let $$ X_n=\sum_{i=0}^n Z_i . $$

Can you show me in details how to calculate $P(X_n \geq a)$ for a certain $a>0$? I thought that it was the case to use the cumulative binomial distribution, but I tried to compare my results with the data I have and they did not match.

As second question, I would appreciate just a little hint on how to compute that probability with excel.

  • 0
    I saw your flag that you wanted to delete this question. I wanted to make the point that this site helps everyone online - even though you've got the answer now, if someone had the same question as you, we'd want them to be able to see the answer here as well. Also, you can write up your solution as an answer; this is explicitly encouraged by the SE network of sites. See [here](http://meta.stackexchange.com/questions/12513/should-i-not-answer-my-own-questions) and [here](http://blog.stackoverflow.com/2011/07/its-ok-to-ask-and-answer-your-own-questions/).2012-06-28

2 Answers 2