Exercise 1 Suppose you have a random sample 1....Un of 100 observations from a normal distribution with unknown mean and unknown standard deviation o. You want to estimate these two parameters using both maximum likelihood estimation (MLE) and method of moments (MoM). 1. Write down the likelihood function for the sample. 2. Using MLE, find the estimates of u and o. 3. Using MoM, find the estimates of u and a. 4. Compare the estimates obtained using MLE and MoM. 5. Can you answer the same questions as above if we assume the random sample is generated from the following density function: f(a; a)= a(a + 1)2-1(1-x)

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