Question

iid Let X1,, X, ^ X~P for some unknown distribution P with continuous cdf F. Below we describe a ? test for the null and alternative hypotheses We divide the sample space into 5 disjoint subsets refered to as bins A1(-00,-2), A2 -(-2,-0.5), As -(-0.5,0.5), A4 (0.5,2) As -(2, oo). as functions of X, by Now, define discrete random variables For example, if Xi --0.1, then Xi є Аз and so Y;-3. In other words, Y, is the label of the bin that contains Xi. By the definition above, iid and Y follows the multinomial distribution on 1,2,3, 4,5 with (vector) parameter p (P P Ps P Ps)E As where p, denote the probability that Y- j. Assume the following special case of the null hypothesis holds: iid ,Xn~N(0, 1 시, What is the vector parameter p As of the multinomial distribution followed by Yi? Fill in the first three entries pi, p2, Ps below.

Answer 1

again p1=.023,p2=.286,p3=.954.

1> Again An 5 P -1