Show transcribed image text 2. Let Xi,., Xn be a random sample from the density 393 )40 f(z,0) = (a) [5 marks] Show that Î¸ explicitly) with Î¸ unknown (actually it is simply hidden to 28 is an unbiased estimator for Î¸ and compute its variance. (b)[7 marks] Write down the expression that leads to the MLE Î¸. (Do not try to find it Column a (see attached) contains 1,000 observations from a specific density f(x, 9) above (c) [5 marks] We want here to (numerically) investigate the variances of the two proposed you). Write a small script that extracts the MLE Î¸ of Î¸. What is the numerical value of Î¸? estimators Î¸ and Î¸. Create a matrix z containing 100 samples, each of size 1,000 from f(,2). How to do this: you first compute the cdf F(,2), invert it, apply the inverse to a (d) (8 marks] (Cont, with part e). Create 200 estimators: Î¸!, ,0100 and 6,, ,0100 matrix y of 100 samples, each of size 1,000 from uniform distribution. from the 100 samples contained in z. Find their sample means, sample biases, and sample in particular, how do they fit with what you were expecting.

2. Let Xi,., Xn be a random sample from the density 393 )40 f(z,0) = (a) [5 marks] Show that Î¸ explicitly) with Î¸ unknown (actually it is simply hidden to 28 is an unbiased estimator for Î¸ and compute its variance. (b)[7 marks] Write down the expression that leads to the MLE Î¸. (Do not try to find it Column a (see attached) contains 1,000 observations from a specific density f(x, 9) above (c) [5 marks] We want here to (numerically) investigate the variances of the two proposed you). Write a small script that extracts the MLE Î¸ of Î¸. What is the numerical value of Î¸? estimators Î¸ and Î¸. Create a matrix z containing 100 samples, each of size 1,000 from f(,2). How to do this: you first compute the cdf F(,2), invert it, apply the inverse to a (d) (8 marks] (Cont, with part e). Create 200 estimators: Î¸!, ,0100 and 6,, ,0100 matrix y of 100 samples, each of size 1,000 from uniform distribution. from the 100 samples contained in z. Find their sample means, sample biases, and sample in particular, how do they fit with what you were expecting.