## Question

###### Let 1.1z. 1 be a random sample of size n from a distribution with probability density functionf(I.a) =a-?re-/a 1 >0. 0 >0(a) Obtain the maximum likelihood estimator of a. 6_ Calculate the estimate whenT10.25. T2 0.75, Iy = 1.50, I4 = 2.5, Is 2.0.(b) Obtain the method of moments estimator of a. a. Calculate the estimate whenT1 = 0.25. T2 = 0.75. I; = L.5O. I4 = 25. IS =20.(Hint for part (b): you can use the first population moment E(X) = Za directly:)

Let 1.1z. 1 be a random sample of size n from a distribution with probability density function f(I.a) =a-?re-/a 1 >0. 0 >0 (a) Obtain the maximum likelihood estimator of a. 6_ Calculate the estimate when T1 0.25. T2 0.75, Iy = 1.50, I4 = 2.5, Is 2.0. (b) Obtain the method of moments estimator of a. a. Calculate the estimate when T1 = 0.25. T2 = 0.75. I; = L.5O. I4 = 25. IS =20. (Hint for part (b): you can use the first population moment E(X) = Za directly:)

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