Binomial Distribution
The binomial distribution describes the behavior of a count variable X if the following conditions apply:
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes ("success" or "failure").
4. The probability of "success" p is the same for each outcome.
If these conditions are met, then X has a binomial distribution with parameters n and p, abbreviated B(n,p).
ex: Suppose individuals with a certain gene have a 0.70 probability of eventually contracting a certain disease. If 100 individuals with the gene participate in a lifetime study, then the distribution of the random variable describing the number of individuals who will contract the disease is distributed B(100,0.7).
Binomial Probability
The probability that a random variable X with binomial distribution B(n,p) is equal to the value k, where k = 0, 1,....,n , is given by
P(X=k) = (n!/k!(n-k)!)pk(1-p)n-k
Properties
1. µ=np
2. σ2=np(1-p)
