The time a customer spends using a service is distributed with pdf f(x) = λ^k x^(k−1)...

The time a customer spends using a service is distributed with pdf f(x) = λ^k x^(k−1) e^(−λx) / (k − 1)! , x ≥ 0. In the pdf there are two parameters: k and λ. You can assume (if you need to) that k is an integer larger than or equal to 1 (k = 1, 2, . . .), and λ is a real, non-negative number (λ ≥ 0). You have been observing a process that is supposed to follow this distribution and have seen 10 customers enter and exit the service: they spend time using the service (in minutes) equal to: 3, 3.3, 13.6, 7.6, 5.4, 7.9, 11.5, 5.4, 13.4, 8.9. Answer the following questions.

(a) Use the method of moments to estimate k and λ.

(b) Find a maximum likelihood estimator for k and λ. [Hint: Find two derivatives, one for each of the parameters.]

Expert Solution

orchestra answered 2 years ago

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