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Problem of the Day #357: Partial Walks March 10, 2012

Posted by Alex in : potd , trackback

Albert is on a very long path which eventually leads to his house. Every second, Albert will walk one step toward his house with a probability of $\frac{1}{x}$, and stop walking entirely with a probability of $\frac{x-1}{x}$. In terms of $x$, what is the expected value of the distance (in steps) that Albert covers?

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