Question: (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

$X$ 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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