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1) (a) (14 pts.) Consider the experiment in which a number is chosen uniformly in (1;...

1) (a) (14 pts.) Consider the experiment in which a number is chosen uniformly in (1; 2; : : : ; 10). Let
event A be the number is divisible by 3, and event B be the number is (strictly-) greater than
5.
(i) Write the sample space S for the aforementioned experiment and express events A and
B as subsets of S.
(ii) Are A and B mutually exclusive? Prove.
(iii) Are A and B statistically independent? Prove.

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