Page 261 - Schaum's Outlines - Probability, Random Variables And Random Processes
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ESTIMATION THEORY [CHAP 7
The likelihood function is given by [Eq. (2.40)]
Thus,
where
and
Setting d[ln L(A)]/dA = 0, the maximum-likelihood estimate A,, of 1 is obtained as
A,, = - xi
n i=l
Hence, the maximum-likelihood estimator of A is given by
7.9. Let (XI, . . . , X,) be a random sample of an exponential r.v. X with unknown parameter A.
Determine the maximum-likelihood estimator of 1.
The likelihood function is given by [Eq. (2.48)]
Thus,
and
Setting d[ln L(R)]/dl = 0, the maximum-likelihood estimate i,, of 1 is obtained as
Hence, the maximum-likelihood estimator of 1 is given by
7.10. Let (XI, . . . , X,) be a random sample of a normal random r.v. X with unknown mean p and
unknown variance a2. Determine the maximum-likelihood estimators of p and a2.
The likelihood function is given by [Eq. (2.52)]
