(b) Let X₁, X₂, ..., X, denote independent and identically distributed random variables from a distribution with pdf giv

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B Let X X X Denote Independent And Identically Distributed Random Variables From A Distribution With Pdf Giv 1 (32.9 KiB) Viewed 9 times

(b) Let X₁, X₂, ..., X, denote independent and identically distributed random variables from a distribution with pdf given by f(x) = (²) rx²-¹e-xr/e, x>0, where > 0 is an unknown parameter and r is a known positive constant. (i) (ii) (iii) Show that the maximum likelihood estimator of 0 is = 1=1 X[ 22 Show that is an unbiased estimator of 0. Given the following observations, find the maximum likelihood estimate of when r is 3: 1.4, 2.3, 3.0, 2.5, 3.5, 4.3 (10 marks)