Binomial probability

• A Bernoulli trial: experiment with 2 outcomes (success, failure)

• A binomial random variable is the outcomes of an n-stage experiment which:

  • each stage is a Bernoulli trial trial with same probability p of success
  • stages are independent
  • the random variable X is the number of successes, not order

• If X is a binomial random variable,

  • n: number of trials
  • p: probability of success

• Binomial distribution with n independent stages is denoted by: $B(n,p)$

• $\mu$ : mean // expected value of x ($E(x)$)

• ${\sigma }^2$: variance

• $\sigma$: standard deviation

• For a binomial random variable $X\sim B(n,p)$ where $q=1-p$

  • $\mu =np$
  • ${\sigma }^2=npq$
  • $\sigma =\sqrt{npq}$