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I have $n$ coins and each of them shows head with probability $p$ if I throw them separately. Now I throw them one-by-one, and each current throw has a correlation $\rho$ with the previous result. (I hope this is rigorously defined through the definition of correlation coefficient.) After one round of tossing, what is the probability that I got $k$ heads in total?

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    Deta$i$ls are all in the answer which used to be here, deleted for lack of interest.2011-02-26

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