Statistics I207910 marksNumerical: fitting Poisson distributionDiscrete distributions
Question Under what conditions does Binomial distribution tend to Poisson distribution? The number of telephone calls received during the month of May is summarized in the following table. Fit the Poisson distribution.
Question
Under what conditions does Binomial distribution tend to Poisson distribution? The number of telephone calls received during the month of May is summarized in the following table. Fit the Poisson distribution.
$$\begin{array}{c|ccccc} \text{Number of telephone calls per day} & 0 & 1 & 2 & 3 & 4 \ \hline \text{Number of days} & 8 & 12 & 18 & 13 & 9 \ \end{array}$$
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Number of calls per day (x) 0 1 2 3 4 ------------------ Number of days (f) 8 12 18 13 9 $N = \sum f = 8 + 12 + 18 + 13 + 9 = 60$ --- The Binomial distribution $B(n, p)$ tends to the Poisson distribution when: 1. Number of trials is very large: $n \to \infty$ 2. Probability of success is very sma...