# Concluding Fall 2008

Thanks all for participating POW actively. Here’s the list of winners:

1st prize:  Yoon, Haewon (윤혜원) – 수리과학과 2004학번

2nd prize: Yang, Hae Hun (양해훈) – 2008학번

3rd prize: Kwon, Sang Hoon (권상훈) – 수리과학과 2006학번

Congratulations!

In addition to those three people, I have selected two students based on the number of solutions they submitted. They will receive 1 movie ticket each.

Kim, Chiheon (김치헌) – 수리과학과 2006학번

Jeong, Seonggu (정성구) – 수리과학과 2007학번

Kim, Jaehoon (김재훈) – 수리과학과 2003학번

will receive one coupon for his participation.

In 2009, I am planning to revise the rule to select winners. Any opinion would be appreciated. Please leave your comment here or email to sangil@.

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# 2008-13 Two i.i.d. random variables

Let X and Y be independent and identically distributed random variables with real values. Prove that if E(X) is finite, then E(|X+Y|)≥E(|X-Y|).

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Find all real numbers $$\lambda$$ and the corresponding functions $$f$$ such that the equation
$$\displaystyle \int_0^1 \min(x,y) f(y) \,dy=\lambda f(x)$$
has a non-zero solution $$f$$ that is continuous on the interval [0,1].