Exercises for Tue Sep 8: ¡­

Exercises for Tue Sep 8:

Extra 4: Let Y1, ... Yn be i.i.d. from the uniform (0, theta) distribution, and let Mn be the largest of these observations. Find the limit distribution of n (theta - Mn), and use this to form an approximate 95% confidence interval for theta.

Extra 5: Suppose Xn and X are variables taking values in 0, 1, 2, ..., with Pr(Xn = j) = pn(j) and Pr(X = j) = p(j). Show (from the start definition) that Xn tends in distribution to X if and only if pn(j) tends to p(j) for all j. Use this to demonstrate that if Xn is Bin(n, p), with np tending to lambda as n increases, then Xn tends to the Poisson (lambda).

Then, from ELL's exercises for Ch 2: 3.1, 3.2, 3.3, 3.6, 3.7, 3.10, 3.12.