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Suppose that 21 observations are taken at random from an
Chapter 7, Problem 15(choose chapter or problem)
Suppose that 21 observations are taken at random from an exponential distribution for which the mean is unknown ( > 0), the average of 20 of these observations is 6, and although the exact value of the other observation could not be determined, it was known to be greater than 15. Determine the M.L.E. of .
Questions & Answers
QUESTION:
Suppose that 21 observations are taken at random from an exponential distribution for which the mean is unknown ( > 0), the average of 20 of these observations is 6, and although the exact value of the other observation could not be determined, it was known to be greater than 15. Determine the M.L.E. of .
ANSWER:Step 1 of 3
Let random variables have joint pdf or pmb
where the parameters are unknown. When function is a function of parameters it is called the likelihood function.
Values that maximize the likelihood function are the maximum likelihood estimates (mle's), or equally values for which
for every . By substituting with , the maximum likelihood estimators are obtained.