Maths a level s2

Level S2

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 independently, 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 either when:

i) n is large and p is close to 0.5. ii) or when np>5 and n(1-p)>5

  1. Normal approximation to Poisson Distribution: Can be used when lambda is greater than 10. Mean = variance = lambda