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Bernoulli

Let X1 , ... , Xn be n independent Bernoulli random variables.Let Y1 , ... , Yn be another n independent Bernoulli random variables. Let X = X 1 + · · · + Xn and Y = Y1 + · · · + Y,.,. Suppose that P(Xi = 1) 2: P(Yi = 1) for all i = 1, 2, ... , n. Does this guarantee that P(X > k) 2>P(Y> k) for all k = 1, 2, ... , n?


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