IMSE2133 Worksheet 7 Latest
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Let 1, 3, 5, 3, 6, 7, 8, 7 be a sample from a random
variable ???? with pdf
????(????) = {
????
????
2
????
?
????
2
2????
2
, 0 < ????
0, otherwise
where ???? > 0 is an unknown parameter.
1. How many parameters are there in the distribution?
Method of moment
2. What is the sample mean?
3. Express ????(????) in term of ????.
4. Find the moment estimator of ????.
IMSE2133 Worksheet 7
Method of maximum likelihood
5. Write the log-likelihood function ????(????).
6. What is the value of ???? such that ????(????) is maximum? (The result is the maximum
likelihood estimator of ????.)
????(????) = {
????
????
2
????
?
????
2
2????
2
, 0 < ????
0, otherwise
where ???? > 0 is an unknown parameter.
1. How many parameters are there in the distribution?
Method of moment
2. What is the sample mean?
3. Express ????(????) in term of ????.
4. Find the moment estimator of ????.
IMSE2133 Worksheet 7
Method of maximum likelihood
5. Write the log-likelihood function ????(????).
6. What is the value of ???? such that ????(????) is maximum? (The result is the maximum
likelihood estimator of ????.)
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