随机算法 (Spring 2013)/Problem Set 1

Problem 1 (10 points)

• Suppose that you are given a coin for which the probability of HEADS, say [math]\displaystyle{ p }[/math], is unknown. How can you use this coin to generate unbiased (i.e., [math]\displaystyle{ \Pr[\mathrm{HEADS}]=\Pr[\mathrm{TAILS}]=1/2 }[/math]) coin-flips? Give a scheme for which the expected number of flips of the biased coin for extracting one unbiased coin-flip is no more than [math]\displaystyle{ \frac{1}{p(1-p)} }[/math].