I have two distributions: $X_1 \sim \mathrm{Binomial}(n_1, p_1)$ and $X_2 \sim \mathrm{Binomial}(n_2, p_2)$; I need to use MLE to find an estimate $\ \hat f$ of $\ f = p_1-p_2$. I know that the answer is $\hat p_1 - \hat p_2$, but I don't understand how to apply MLE in this case. Surely we can't write down the likelihood as a product of probabilities since we're not dealing with a single distribution but with two different ones?
2026-03-30 09:35:58.1774863358
How can I use MLE to find an estimate of a difference of proportions?
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