Estimating the probability $p$ of heads for a coin from $7$ heads in $10$ independent flips
Terms
| Term | This example | Why |
|---|---|---|
| maximum likelihood estimator | $\hat{p} = 0.7$ | The maximum likelihood estimate of the probability of heads from $7$ heads in $10$ flips is $\hat{p} = 0.7$, because the likelihood $L(p) = p^7 (1 - p)^3$ has the derivative $p^6 (1 - p)^2 (7 - 10 p)$, which is zero at $p = 7/10$, where $L$ is largest. |