Suppose that Dan is asked to estimate the distribution of su

Suppose that Dan is asked to estimate the distribution of successive times between calls, placed to a call center. (A call center is a service operation that answers 1-800 or 1-866 calls.) The collected data is: 10, 10, 30, 10, 20, 50 (measured in seconds), where the call logging system takes a call with duration x and “rounds up” to the next multiple of 10 seconds (i.e., a call of duration x is logged as 10x/10, where y is the “ceiling” of y, defined as the least integer greater than or equal to y). Help Dan estimate the distribution, assuming that it is exponential.

a.) Show that P (Yi = 40) = P (30 < Xi 40) = e(y10)|y=30 e(y10)|y=40 where is the rate of exponential distribution.

b.)Help Dan estimate the distribution, assuming that it is exponential.

Solution