Could someone clarify if I'm interpreting this question correctly?
As the sample size increases and approaches infinity, then the expected value of the estimator would approach $0.$ The estimator is biased because $θ$ is not equal to $θ/n.$
But, if $n = 1,$ then wouldn't the expected value${} = θ$? Is this how the statistician's estimator would become unbiased?
Clarification appreciated!
We don't have to take limit of $n$ to $\infty$, currently we have
$$\mathbb{E}[\hat{\theta}]=\frac{\theta}{n}$$
We want to find $k$ such that
$$\mathbb{E}[k\hat{\theta}]=\frac{k\theta}{n}=\theta$$
Can you solve for $k$?