Let \(n\) be a fixed positive integer and let \(p\in (0,1)\). Let \(D_n\) be the determinant of a random \(n\times n\) 0-1 matrix whose entries are independent identical random variables, each of which is 1 with the probability \(p\) and 0 with the probability \(1-p\).  Find the expected value and variance of \(D_n\).

The best solution was submitted by Myeongjae Lee (이명재), 2012학번. Congratulations!

Here is his Solution of Problem 2012-21.

Alternative solutions were submitted by 박민재 (2011학번, +3), 김태호 (수리과학과 2011학번, +3), 임현진 (물리학과 2010학번, +3), 김지홍 (수리과학과 2007학번, +2), 서기원 (수리과학과 2009학번, +2).