Binomial distribution expectation

To find the expectation (mean) of a binomial distribution, we multiply the number of trials by the probability of success.

\text{for }X\sim B(n,p) \quad E(X)=np

• E(X) is the expectation of the discrete random variable X
• n is the number of trials
• p is the probability of success [in each trial].

Explaining the formula

If you toss a fair coin 100 times, you can expect to get 50 heads. Because the number of trials is 100 and the probability is 0.5, so you do 100\times0.5=50 - multiply the number of trials by the probability of success of each trial.

To round or not to round

The expected outcome can (and often is) a decimal! Even if it’s not possible to get that expected value (because the binomial distribution works on discrete values) you should still give the (impossible) decimal answer, as that’s the mean and expectation.