BINOMIAL DISTRIBUTION

Always has two outcomes, success and failure

X ~B (n, p)

n = fixed No. of trials, they are independent

p = prob of success

q = prob of failure

Mean = E(X) = m = np

Variance = Var(X) = s² = np(1- p) = npq

Probability of r successes

P( X = r ) = n p^r q^n-r or use tables

r

Approximation

Normal approx Þbinomial X ~B (n, p) ÞX ~N (np , npq)

1. n large

2. np > 5

3. nq > 5

Poisson approx Þbinomial X ~B (n, p) ÞX ~P_o (np)

1. n large

2. p small