6. Let X be a random variable with a uniform distribution on the finite interval [-1, 0], where # > -1 is unknown. Suppose that a random sample of size n is drawn from the distribution, with observations r1, . .., In- Write down the likelihood function for the parameter 0, and find the maximum likeli- hood estimate (MLE) for 0. Solution: The likelihood function is C= (0 + 1 )n The likelihood is maximized when (0 + 1) is minimized. The possible estimates are constrained by the data, which respects -1