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Unformatted text preview: d that we would like to generate Bernoulli random
variables with parameter p = 0.5 using ﬂips of a biased coin. That is, suppose that the probability
the coin shows H (for heads) is a, where a is some number that might not be precisely known.
Explain how this coin can be used to generate independent Bernoulli random variables with p = 0.5.
Solution: Here is one solution. Flip the coin repeatedly, and look at the outcomes two at a time.
If the ﬁrst two outcomes are the same, ignore them. If they are diﬀerent, then they are either HT (a
head followed by a tail) or T H . In this case, give as output either H or T , whichever appeared ﬁrst
in those two ﬂips. Then repeat this procedure using the third and fourth ﬂips, and so fourth. One
might wonder how many times the biased coin must be ﬂipped on average to produce one output.
The number of pairs of ﬂips has the geometric distribution, with parameter 2a(1 − a). Therefore,
the mean number of pairs of coin ﬂips required until an HT or T H is observed...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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