MATH STATISTICS

1. Let X ~ N(0, 1), Y := I(x>1} - I(x

1. Let X N(0, 1), Y - and Z X Y. Define the matrix A by (a) Find the distribution of Y and the distribution of Z and classify them as discrete, absolutely continuous, or neither. (b) What is the probability distribution of det(A)? (c) Find P ( {A is invertible}). (5) (3) (2) [10]