Question: 5. (MOM and MLE, 20 points) [The following example shows that sometimes only using first moment may not be sufficient, higher moments are needed.] Let

5. (MOM and MLE, 20 points) [The following example shows that sometimes only using first moment may not be sufficient, higher moments are needed.] Let X1, ..., Xn be independent identically distributed random variables with probability density function f (x) = 1 20 exp ,-DO 0 is some unknown parameter. This is known as the Laplace distribution or double exponential distribution. (a) Find the moment estimator of o. (b) Find the maximum likelihood estimator of o

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