Question

Let Xi,, Xn be a random sample of size n from the normal distribution with mean parameter 0 and variance σ2-3. (a) Justify thatX X, has a normal distribution with mean parameter 0 and variance 3 /n, this is, X~N(0,3/m) (you can do it formally using m.g.f. or use results from normal distribution to justify (b) Find the 0.975 quantile of a standard normal distribution (you can use a table, software or internet to find the quantile). (c) Find the distribution of(you can use m.g.f., transformation theorem or justify using results from the normal distribution). (d) Find the size of a random sample, n, such that the probability of the absolute difference between and θ being equal or smaller than 0.5 is at most 0.95.

Answer 1