Two Cars and the Arrival Rate

Cars pass a roadside sensor as a Poisson process with unknown rate $\lambda$ per second, so the gaps between arrivals are independent exponentials. You start watching at time zero. The first car passes at $t = 4$ seconds and the second at $t = 10$ seconds. (a) What is the maximum-likelihood estimate of $\lambda$? (b) Is that estimator unbiased? If not, produce one that is.