Assume you have an unfair coin - the one that lands heads with probability P (not known beforehand). You have rolled such a coin 20 times and got 16 heads and 4 tails. What is the best estimator of P, Pˆ? (Hint: it is the one based on sample mean.)
To find the best estimator of P, we need to use the sample mean. The sample mean is the sum of the outcomes divided by the number of trials. In this case, we have rolled the coin 20 times and obtained 16 heads and 4 tails.
The sample mean, denoted as P̂ (pronounced "P-hat"), is calculated by dividing the total number of heads by the total number of trials. In this case, P̂ is equal to 16 (number of heads) divided by 20 (total number of trials).
So, P̂ = 16/20 = 0.8
Therefore, the best estimator of P, based on the given sample, is P̂ = 0.8.