Conditions for a Binomial Distribution
- There must be a fixed number of trials.
- Trials must be independant.
- The trials must have 2 outcomes, success or failure.
- The probability of success must be constant for every trial.
Conditions for a Poisson Distribution
Events occur independently, at a constant rate, and singly in continuous space or time.
Approximations using different Distributions
- 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.
- Normal approximation to Binomial Distribution: N(np, np(1-p)) can be used either when:
i) n is large and p is close to 0.5. ii) or when np>5 and n(1-p)>5
- Normal approximation to Poisson Distribution: Can be used when lambda is greater than 10. Mean = variance = lambda