Description
Problem 1. Assume a SRS X1,··· ,Xn from the population random variable X having uniform distribution U(0,θ) with some θ > 0.
- Find the moment estimator θˆM;
- Find the maximum likelihood estimator θˆL;
- 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 θˆM and θˆL. Which one is better? Why?
- For θ = 7, generate 100 SRS’s of size n = 30, evaluate the observed values of θˆM and θˆL. Produce box plot and mark the sample mean of the corresponding observed values of θˆM and θˆL, respectively.
- For θ = 7, generate a SRS of size n = 20,30,50,100,150, evaluate the observed values of θˆM and θˆL. Plot the corresponding observed values of θˆM and θˆL, respectively.
Problem 2. Assume a SRS X1,··· ,Xn from the population random variable X ∼ N(µ,σ2).
- Find the moment estimator (ˆµ,
- Find the maximum likelihood estimator (˜µ,
Problem 3. Finish the following problems in the textbook:
Exercises 6.17, 6.27 and 6.28.
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