Let X, X, be i.i.d. random variable with density function f(x 0) (0 +1)x, 0 x...

 

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Let X, X, be i.i.d. random variable with density function f(x 0) (0 +1)x, 0 x 1. = ... (a) (5%) Find the mean of a random variable with the above density function. (b) (5%) Find the method of moment estimate of 0. (c) (5%) Find the mle of 0. (d) (5%) Find the asymptotic variance of the mle. (e) (5%) Derive a 100(1 - a) % asymptotic confidence interval for 0. Let X, X, be i.i.d. random variable with density function f(x 0) (0 +1)x, 0 x 1. = ... (a) (5%) Find the mean of a random variable with the above density function. (b) (5%) Find the method of moment estimate of 0. (c) (5%) Find the mle of 0. (d) (5%) Find the asymptotic variance of the mle. (e) (5%) Derive a 100(1 - a) % asymptotic confidence interval for 0.