Lecture 3 - Ch 5 - Binomial Distribution

The binomial distribution is used to describe a discrete random variable under these conditions:

1. An experiment is repeated several times - n
2. Each "experiment" has two possible outcomes - success/failure, heads/tails, etc
3. The probability of the two outcomes is constant across the experiments
4. Each outcome is statistically independent of the others. Like when you flip a coin, the chances of heads on the 100th flip are 50/50 even if you had 99 tails in a rows before it. (Although if that really happened, I'd check the coin!)
   

In a scenario that fulfills those conditions, the probability of obtaining x successes in n experiments is:where

x = the number of successes
n = the number of experiments/trials/observations
p = the probability of success in any single experiment/trial/observation

The mean of the binomial distribution is np.
The standard deviation of the binomial distribution is np(1-p).