## Math T Coursework Term 3 Sample Question

Sample Question

Binomial distribution may be approximated, under certain circumstances, by Poisson distribution or normal distribution. One practical advantage is that the calculations for finding probabilities are much less tedious to perform.

1. Consider a random variable having binomial distribution B(n, p).

(a) Let p=0.05 and n=5, 10 and 20. Tabulate all the probabilities using binomial distribution, Poisson distribution and normal distribution. (Note: For n=5. manual calculations must be used)

(b) Repeat step 1(a) for p = 0.1 and 0.5.

2

(a) Illustrate graphically the probability distributions.

(b) Compare the probability distributions obtained and discuss your findings.3. Investigate what happens when n increases.

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