Let X1, . . ., Xn be a random sample from U (0, ) distribution. Let Yn = max {X1, . . ., Xn}. We

Let X1, . . ., Xn be a random sample from U (0, θ) distribution. Let Yn = max {X1, . . ., Xn}. We know (from Example 5.3.4) that θ-cap1 = θn is a MLE of θ.
(a) Show that θ-cap2 = 2X-bar is a method of moments estimator.
(b) Show that θ-cap1 is ,a biased estimator, and θ-cap2 is an unbiased estimator of θ.
(c) Show that θ-cap3 = n + 1/N θ-cap1 is an unbiased estimator of θ.