I just found it very cool that Monte Carlo Estimator is still unbiased regardless of where we sample in the distribution. However, we can have a very inaccurate Monte Carlo estimator depending on where we sample the distribution still (such as sampling all in the same local area instead of the entire distribution).
@jerryzhucs21 good observation! Another way to see this mathematically is to look at the variance of the monte carlo estimator.
Monte Carlo estimator is also low-varianced if we have sufficient samples.