Let = [0, ) be a sample space and let F be the sigma field of...

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Let = [0, ∞) be a sample space and let F be the sigma field of subsets of generated by all sets of the form (n,n+1) for n 1,2,... = A (a) Are Are the following subsets of in F? (i) [0,00), (ii) Z+= [0,1,2,...), (iii) [0,k]U[k +1,∞) for any positive integer 2+ k, (iv) [k] for any positive integer k, (v) [0,k] for any positive integer k, (vi) (1/3,2). Let = [0, ∞) be a sample space and let F be the sigma field of subsets of generated by all sets of the form (n,n+1) for n 1,2,... = A (a) Are Are the following subsets of in F? (i) [0,00), (ii) Z+= [0,1,2,...), (iii) [0,k]U[k +1,∞) for any positive integer 2+ k, (iv) [k] for any positive integer k, (v) [0,k] for any positive integer k, (vi) (1/3,2).