Question

Let $X_1, X_2, dots, X_n$ be a random sample (i.e i.i.d.) form the distribution with p.d.f. $ heta qquad f_ heta(x) = egin{cases} frac{ heta}{x^{( heta+1)}} & ext{if } x > 1\ 0 & ext{otherwise.} end{cases}$ where $ heta > 0$ is unknown. (a) (5 points) Determine the MLE of $ heta$. (b) (6 points) Find a minimal sufficient statistic for the model.

          Let $X_1, X_2, dots, X_n$ be a random sample (i.e i.i.d.) form the distribution with p.d.f.
$	heta
qquad f_	heta(x) = egin{cases} frac{	heta}{x^{(	heta+1)}} & 	ext{if } x > 1\ 0 & 	ext{otherwise.} end{cases}$
where $	heta > 0$ is unknown.
(a) (5 points) Determine the MLE of $	heta$.
(b) (6 points) Find a minimal sufficient statistic for the model.

$Let X1, X2, dots, Xn be a random sample (i.e i.i.d.) form the distribution with p.d.f. heta qquad f heta(x) = egincases frac hetax^( heta+1) extif x > 1 0 extotherwise. endcases where heta > 0 is unknown. (a) (5 points) Determine the MLE of heta. (b) (6 points) Find a minimal sufficient statistic for the model.$

Added by Montserrat O.

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