Question

Let X1 Xn be a random sample from a distribution with the pdf f(x(9) = θ(1 +0)-r(0-1) (1-2), 0 < x < 1, θ > 0. the estimator T-4 is a method of moments estimator for θ. It can be shown that the asymptotic distribution of T is Normal with ETT θ and Var(T) 0042)2 Apply the integral transform method (provide an equation that should be solved to obtain random observations from the distribution) to generate a sam ple of size n 100 from the distribution with θ 2.5. Use the large sample theory for MLE to compute a 95% confidence interval for θ based on the random sample 2n (0+3)

Answer 1

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04141 +3 431 61203 >イ 9t) (013) (831 043) (013) (era) (013)

912 (3) (812) 912 (843) (642) 042 (0+ (43) 0+2 (042) 05 2 5+2 (2.stg)"( 25t3%σο } 2.다2
thank you