Consider a random sample X, X2,....X, from the shifted exponential pdf x; A, 0) = {Ae-N Ae-Ax-) x0 otherwise Taking 60 gives the pdf of the exponential distribution considered previously (with positive density to the right of zero). An example of the shifted exponential distribution appeared in Example 4.5, in which the variable of interest was time headway in traffic flow and 0.5 was the mini- mum possible time headway.

a. Obtain the maximum likelihood estimators of 0 and A.

b. If n = 10 time headway observations are made, result- ing in the values 3.11, .64, 2.55, 2.20, 5.44, 3.42, 10.39, 8.93, 17.82, and 1.30, calculate the estimates of and A.