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 variableX n is the number of trialsp 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
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.
flashcards
| Question | Answer |
|---|---|
| For | |
| How do you calculate the expectation of a binomial distribution? | Multiply the number of trials by the probability of success. |
| If you toss a fair coin 100 times, what is the expected number of heads? | |
| What should you do if the expected value of a binomial distribution is a decimal? | Give the decimal answer, even if it’s not possible to obtain that value, because it’s the mean. |