STAT 100A HWI Due next Wed in classProblem 1:Suppose we flip a fair coin 4 times independently.(1) What is the sample space?(2) What is the set that corresponds to the event that the number of heads is 2? What is itsprobability?(3) LetZi= 1 if thei-th flip is head, andZi= 0 otherwise, fori= 1,2,3,4. LetXbe thenumber of heads. ExpressXin terms ofZi.(4) What is the probability distribution ofX? That is, what is Pr(X=k) fork= 0,1,2,3,4?Problem 2:Suppose we roll a fair die twice independently. LetXandYbe the two numbers weget.(1) What is the sample space? LetAbe the event thatX >4, andBbe the event thatY >4.What are Pr(A), Pr(B)?(2) LetCbe the event that min(X, Y)>4? What is Pr(C)? What is the relationship betweenPr(C) and Pr(A), Pr(B)?(3) LetDbe the event that max(X, Y)>4? What is Pr(D)? What is the relationship betweenPr(D) and Pr(
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