Maths A Level S2

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Conditions for a Binomial Distribution

1. There must be a fixed number of trials.
2. Trials must be independant.
3. The trials must have 2 outcomes, success or failure.
4. The probability of success must be constant for every trial.

Conditions for a Poisson Distribution

Events occur independantly, at a constant rate, and singly in continuous space or time.

Approximations using different Distributions

1. Poisson approximation to Binomial Distribution: Can be used when n (no. of trials) is large (>75) and when p (probability of success) is small. Po(np) is used.
2. Normal approximation to Binomial Distribution: N(np, np(1-p)) can be used when n is large and p is close to 0.5.
3. Normal approximation to Poisson Distribution: Can be used when lambda is greater than 10. Mean = variance = lambda