STATS 1 HW 1 Please show all your work Answers without suppo

STATS 1 HW 1 Please show all your work Answers without supporting work Name:________ 1. Let (a) Ck = {x : 1/k+1

Solution

(a) This will be (0,1] . Note that any point x in this range (0,1] is contained in atleast one of Ck (for k high enough, we can have x>=(1/(k+1)) ) Also. any point in Ck is contained in range (0,1]. Thus (0,1] is equivalent to given union

(b) This intersection only contains zero. The reason is that for any point, say x>0, is we can have k large enough such that x>1/k0 => x is not in set C_k0 => x is not in the intersection. This is true for any x not equal to zero. But fortunately all sets contain zero. Thus the answer is {0}