Speaker: Prof. Shoou-Ren Hsiau (National Changhua University of Education)
Title: On the Shoe-Door Problem
Time: 2015-01-22 (Thu.)  15:00 - 16:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: A man has a house with $n$ doors. He places one pair of walking shoes at each door. For each walk, he chooses one door at random and puts on a pair of shoes. After the walk he returns to a randomly chosen door and takes off the shoes at the door. Let $N$ represent the number of finished walks until the man discover that no shoes are available at the door he has chosen for a further walk. We are interested in the limiting behavior of $E(N)$ when $n$ is large. In fact, we can prove that $E(N)$/$\sqrt {n}$ $\rightarrow$ $\sqrt{\frac\pi2}$ as $n$ $\rightarrow$ $\infty$.
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