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Let's $X_1 \sim Binomial(n_1, p_1), X_2 \sim Binomial(n_2, p_2)$. I want to find MLE of $\psi = p_1 - p_2$. There is a property of MLE: if $\hat{\theta}$ is MLE of $\theta$, then $g(\hat{\theta})$ is MLE of $g(\theta)$. Is it correct saying that $\hat{p_1} = \overline{X_1}$, $\hat{p_2} = \overline{X_2}$ then $\hat{\psi} = \overline{X_1} - \overline{X_2}$?

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