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An integer N is chosen from 1 to 10 uniformly at random. Two random variables are...

An integer N is chosen from 1 to 10 uniformly at random.

Two random variables are defined: X is 1 plus the remainder on division of N by 3. So e.g. when N = 5, the remainder on division by 3 is 2, so X = 3.

Y is dN/3e. So e.g. when N = 5, Y = 2.

(a) Find E[X], E[Y ] and Var[Y ].

(b) Are X and Y independent?

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