(1 point) The headway between two vehicles passing a point is the time (in seconds) between the two vehicles passing the point as measured from the first front bumper to the second front bumper. That is, the headway is the sum of the time used by the first vehicle to pass the observation point and the time to the arrival of the next vehicle. One model proposed for headway times is the "offset" Exponential distribution, defined for some _ > 0 by the c.d.f. F(x) =1-e-*(x-L) for x > L and some 1 > 0. A study on traffic on a highway with low traffic density aimed to investigate models for headway times. Headway times were collected on data entering a tunnel on the highway over a two-day period. Part of the data are provided below: 30.74, 0.5, 11.64, 37.58, 9.14, 8.03, 0.31, 1.13, 12.59, 1.76, 1.3, 5.62. A offset Exponential distribution model can be assumed here. Provide answers to the following to three decimal places. Part a) Evaluate the log-likelihood function for the data when 1 = 0.0785 and L = 0.24. Part b) Find the maximum likelihood estimate of L. Part c) Hence find the maximum likelihood estimate of 1