Problem 15. (2.5 %) Suppose X is uniformly distributed over [0,4] and Y is uniformly distributed over [0,1]. Assume X and Y are independent. Let Z = X + Y. Then (i) fz(4.5)=0 (ii) fz(4.5)=1/8 (iii) fz(4.5) =1/4 (iv) fz(4.5)=1/2

Problem 7. (2.5 %) Consider two random variables X and Y, each taking val- ues in {1,2,3}. Let their joint PMF be such that for any 1 ≤ x, y ≤ 3,Then, (i) X and Y can be independent or dependent depending upon the strictly positive values(ii) X and Y are always independent(iii) X and Y can never be independent

Problem 15. (2.5 %) Suppose X is uniformly distributed over [0,4] and Y is uniformly distributed over [0,1]. Assume X and Y are independent. Let Z = X + Y. Then
(i) f_z(4.5)=0
(ii) f_z(4.5)=1/8
(iii) fz(4.5) =1/4
(iv) fz(4.5)=1/2

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