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2. Let $X_1, dots, X_n$ be a random sample from distributions with the given probability density functions. In each case, find the maximum likelihood estimator. egin{enumerate} item $f(x; heta) = frac{1}{ heta^2}xe^{-x/ heta}, quad 0 < x < infty, quad 0 < heta < infty$ item $f(x; heta) = frac{1}{2 heta^3}x^2e^{-x/ heta}, quad 0 < x < infty, quad 0 < heta < infty$ end{enumerate}

          2. Let $X_1, dots, X_n$ be a random sample from distributions with the given probability density
functions. In each case, find the maximum likelihood estimator.
egin{enumerate}
    item $f(x;	heta) = frac{1}{	heta^2}xe^{-x/	heta}, quad 0 < x < infty, quad 0 < 	heta < infty$
    item $f(x;	heta) = frac{1}{2	heta^3}x^2e^{-x/	heta}, quad 0 < x < infty, quad 0 < 	heta < infty$
end{enumerate}

$2. Let X1, dots, Xn be a random sample from distributions with the given probability density functions. In each case, find the maximum likelihood estimator. eginenumerate item f(x; heta) = frac1 heta^2xe^-x/ heta, quad 0 < x < infty, quad 0 < heta < infty item f(x; heta) = frac12 heta^3x^2e^-x/ heta, quad 0 < x < infty, quad 0 < heta < infty endenumerate$

Added by Laura S.

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