Find an unbiased estimator

Question

Let $X$ be an r.v defined by $P(X=0)=p$ and $P(X=1)=1-p$. Find an unbiased estimator for $2p$. My solution: $E(X)=1-p$ so $2-2E(X)$ is unbiased. Is this correct?

Answer 1

Not quite. An estimator is a statistic, but what you have written, $2 - 2 {\rm E}[X]$, is a function of a random variable. If you have a sample $(x_1, x_2, \ldots, x_n)$ of IID observations from $X$, then what function of this sample will be an estimator for $2p$?