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

- An experiment is repeated several times - n
- Each "experiment" has two possible outcomes - success/failure, heads/tails, etc
- The probability of the two outcomes is constant across the experiments
- 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!)

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).

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