Would this be inconsistent and not unbiased? Because for one point, the estimator would only be unbiased and consistent if the image was just one color.

Cake

I believe it's inconsistent because I_n does not approach I as n-> infinity (since we always only take a single random sample).

keenan

It's also unbiased because the expected value is the correct value, i.e., if we compute this estimate many times and average the results, we will get the correct integral (because we're effectively just applying standard Monte Carlo).

Would this be inconsistent and not unbiased? Because for one point, the estimator would only be unbiased and consistent if the image was just one color.

I believe it's inconsistent because I_n does not approach I as n-> infinity (since we always only take a single random sample).

It's also unbiased because the expected value is the correct value, i.e., if we compute this estimate many times and average the results, we will get the correct integral (because we're effectively just applying standard Monte Carlo).