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