Question: Let X1, X2, . . . Xn be a random sample of size n from a distribution with probability density function f(x, ?) = ?

Let X1, X2, . . . Xn be a random sample of size n from a distribution with probability density function f(x, ?) = ? ?2xe?x/?, x > 0, ? > 0

(a) Obtain the maximum likelihood estimator of ?, ??. Calculate the estimate when x1 = 0.25, x2 = 0.75, x3 = 1.50, x4 = 2.5, x5 = 2.0.

(b) Obtain the method of moments estimator of ?, ??. Calculate the estimate when 1 x1 = 0.25, x2 = 0.75, x3 = 1.50, x4 = 2.5, x5 = 2.0

Let X1, X2, . . . Xn be a random sample of size n

Exercise 2 113*. thzpuxn he a rundmnmmph: [:me nfmmadstbutiun with probability dim-city mct'mn L-u} = a'lre'n. :: :h D. a 3:- {I {3} Obtain the maximum likelihuud zsnmlar aft], Er. anlaie the unmh: when II = \".25? :1 =i.'}.?'..l"r1 3 = LEI], .174 = 2l+ 15 = 2.\". {a} Obtain the method of Imam estimawr of :1. Hr. Calculate u- minmu when 11:11.25, I: = I035, In =1.5l'.|. :4. = 2.5, 15 = 2."

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