(X) have a binomial distribution with parameters (n) and (p). Compare the following exact probabilities with the...

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\(X\) have a binomial distribution with parameters \(n\) and \(p\). Compare the following exact probabilities with the corresponding Poisson approximations and give reasons for possible larger deviations:

(1) \(P(X=2)\) for \(n=20, p=0.1\),

(2) \(P(X=2)\) for \(n=20, p=0.9\),

(3) \(P(X=0)\) for \(n=10, p=0.1\),

(4) \(P(X=3)\) for \(n=20, p=0.4\).

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