Distributionshard
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For XBinomial(n,p)X \sim \text{Binomial}(n, p), the probability P(Xk)P(X \ge k) can be expressed using the regularized incomplete Beta function Ix(a,b)I_x(a, b), which is the CDF of a Beta(a,b)(a, b) distribution. Which of the following is the correct identity?