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I have a probability space $\omega = 2^{\{1,\ldots,n\}}$ $\sigma$-algebra $2^\omega$ and $P(\{s\})=(p^{|s|})*(1-p)^{(n-|s|)}$

I assume that $n=2k$,$k$ natural number

I need to find a random variable that will distribute like $\mathrm{Bin}(k,p^2)$

Can you help me with this please?

Thanks.
benny

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up vote 1 down vote accepted

Hint: $2 = n/k$.

Another hint: $p^2$ has the same exponent $2$ as $n/k$.

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can't figure out how that helps – benjamin Nov 20 '10 at 19:00
    
added another hint. of course, you can't expect us to solve the exercise for you. – Yuval Filmus Nov 20 '10 at 19:30

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