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2 Let X1, X2, ..., X., be independent continuous random variables from the following distribution: f(x)=ox-(-V where = 1 and
2.1 Show that the maximum likelihood estimator of a isante = sok X.
2.2 Show that the method moment estimator for a is: & mom = 1
2.3 Derive a sufficient statistic for a. What theorem are you using to determine sufficiency?
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Answer #1

Xe, x, ... Xn continuou random variables where x7,1 and a71 Given E(X) = x f(x)= xx (x-1) dh = 0 dlogl zo da ca 1) MLE u foun2.) MOM estimator is found by equating x = f(x) Given E(X)= x-1 x = x » (2-1) X=4 = xĂ - x = x = x(x-1) = x 1x lxlik L MOM х3) By füher Neymani factorization theorem to identify sufficient statistic A statutic Tú sufficient for oa) f(x,x ... xulo) =

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