Suppose that X is a Poisson random variable with parameter ?, and k < ?. Show that P{X ? k} ? (e^-? * (e?)^k) / k^k.
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This can be written as the sum of the probabilities for all values less than k: P(X < k) = Σ P(X = i) for i = 0, 1, ..., k-1 Now, let's multiply both sides of the inequality by e^(-A) * e^(A) * k: e^(-A) * e^(A) * k * P(X < k) < e^(-A) * e^(A) * k * k^k Now, Show more…
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