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Statistics / Probability and Statistics 4 / Chapter 7.6 / Problem 4

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

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Suppose that the lifetime of a certain type of lamp has an

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QUESTION:

Suppose that the lifetime of a certain type of lamp has an exponential distribution for which the value of the parameter is unknown. A random sample of n lamps of this type are tested for a period of T hours and the number X of lamps that fail during this period is observed, but the times at which the failures occurred are not noted. Determine the M.L.E. of based on the observed value of X.

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QUESTION:

Suppose that the lifetime of a certain type of lamp has an exponential distribution for which the value of the parameter is unknown. A random sample of n lamps of this type are tested for a period of T hours and the number X of lamps that fail during this period is observed, but the times at which the failures occurred are not noted. Determine the M.L.E. of based on the observed value of X.

ANSWER:

Step 1 of 4

Random variable with pdf

is said to have exponential distribution with parameter .

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