Let $Y$ be independent and identically distributed normal with mean $2\mu$ and variance $16$.
Show that $\frac{\bar y}{2}$ is the maximum likelihood estimator of $\mu$.
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Sign up to join this communityLet $Y$ be independent and identically distributed normal with mean $2\mu$ and variance $16$.
Show that $\frac{\bar y}{2}$ is the maximum likelihood estimator of $\mu$.
You can use invariance property of Maximum Likelihood estimator:
http://en.wikipedia.org/wiki/Maximum_likelihood
If alpha_hat=g(theta_hat) then theta_hat is MLE for alpha_hat.
And notice that 1/2 is jacobian for transformation of alpha=2*theta and average of y is MLE for myy.
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