[Solved] MA331 Homework 03

Problem 1. Assume a SRS X₁, ,X_n from the population random variable X having uniform distribution U(0,) with some > 0.

• Find the moment estimator _M;
• Find the maximum likelihood estimator _L;
• For the real data (X₁, ,X₇) = (1.0,2.4,3.2,1.2,0.5,3.1,6.8), evaluate the observed values of _M and _L. Which one is better? Why?
• For = 7, generate 100 SRSs of size n = 30, evaluate the observed values of _M and _L. Produce box plot and mark the sample mean of the corresponding observed values of _M and _L, respectively.
• For = 7, generate a SRS of size n = 20,30,50,100,150, evaluate the observed values of _M and _L. Plot the corresponding observed values of _M and _L, respectively.

Problem 2. Assume a SRS X₁, ,X_n from the population random variable X N(,²).

• Find the moment estimator (,
• Find the maximum likelihood estimator (,

Problem 3. Finish the following problems in the textbook:

Exercises 6.17, 6.27 and 6.28.