Let X1, ...,Xn be a random sample from the distribution uniform on the union of the two intervals: [2, 1] and [0, ]. Find: (i)

Let X1, ...,Xn be a random sample from the distribution uniform on the union of the two intervals: [−2, −1] and [0, θ]. Find: (i) The MME of θ. (ii) The MLE of θ.

(iii) The MLE of θ if positive Xi’s are recorded exactly, and negative Xi’s can only be counted. (iv) The MLE of θ if Xi’s cannot be observed, and one can only count the numbers of positive and negative ones.