Attached is my working.
As I've labelled, I'm not sure how to get to the answer from my expected value notation. Can somebody help?
2026-03-25 06:28:05.1774420085
How to Adjust Estimator to Make Unbiased?
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In the original question, it is statement that
$$\mathbb{E}[\hat{\theta}]=\theta + \frac1n$$
Hence we have
$$\mathbb{E}\left[\hat{\theta}- \frac1n\right]=\theta $$
I think your msitake is misread the question $\theta + \frac1n$ as $\frac{\theta+1}{n}$.