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Math Help - a binomial distribution proof

  1. #1
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    a binomial distribution proof

    Show that if X~ B(n,p), then

    P(X=x+1)=((n-x)/(x+1))*(p/(1-p))*P(X=x), and x=0,1,2, ..., n-1
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  2. #2
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    Quote Originally Posted by shawli View Post
    Show that if X~ B(n,p), then P(X=x+1)=((n-x)/(x+1))*(p/(1-p))*P(X=x), and x=0,1,2, ..., n-1
    Recall that P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}
    Now observe that \left(\frac{p}{1-p}\right) \left(\frac{n-x}{x+1}\right)P(X=x)=\left(\frac{p}{1-p}\right) \left(\frac{n-x}{x+1}\right)\binom{n}{x}p^x(1-p)^{n-x}
    Now combine and reduce to get to the LHS.
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