A group occurs when the inside if statement is executed. If a list containing a

Question

A group occurs when the inside if statement is executed. If a list containing a random of three distinct integers is passed to bubble sort, give the probability mass of the number of swaps required by the algorithm to wit the random permutation. A fair green die and a fair red die are tossed together. Let X denote the number of sports showing on the green die and Y denote the number of sports showing on the red die Bad the probability mass function for: the sum of the spots show mg on the two dice. X + Y. the number of spots showing on the green die minus the number of sports showing on the red die, X - Y. the difference between the spots showing on the two dice. |X > Y|. the maximum number of spots showing on a single die. max (X, Y). the the minimum number of spots showing on a single die. min {X, Y}.

Explanation / Answer

Probability mass function of X+Y.

Possible values of X+Y = 2,3,4,5,6,7,8,9,10,11,12

The following table provides the pmf

Possible values of X-Y :-5,-4,-3,-2,-1,0,1,2,3,4,5.The PMF is given below in the table

Possible values of |X-Y| = 0,1,2,3,4,5

Possible values of Max(X,Y) = 1,2,3,4,5,6

Following table provides the PFM of MAX(X,Y)

Min{X,Y}

Possible values of Min(X,Y) = 1,2,3,4,5,6

Follwoing tble provides the PFM of Min(X,Y)

Green Die:X Red Die:Y X+Y Green Die:X Red Die:Y Sorted:X+Y X+Y P(X+Y) 1 1 2 1 1 2 2 1/36 1 2 3 1 2 3 3 2/36 1 3 4 2 1 3 4 3/36 1 4 5 1 3 4 5 4/36 1 5 6 2 2 4 6 5/36 1 6 7 3 1 4 7 6/36 2 1 3 1 4 5 8 5/36 2 2 4 2 3 5 9 4/36 2 3 5 3 2 5 10 3/36 2 4 6 4 1 5 11 2/36 2 5 7 1 5 6 12 1/36 2 6 8 2 4 6 3 1 4 3 3 6 3 2 5 4 2 6 3 3 6 5 1 6 3 4 7 1 6 7 3 5 8 2 5 7 3 6 9 3 4 7 4 1 5 4 3 7 4 2 6 5 2 7 4 3 7 6 1 7 4 4 8 2 6 8 4 5 9 3 5 8 4 6 10 4 4 8 5 1 6 5 3 8 5 2 7 6 2 8 5 3 8 3 6 9 5 4 9 4 5 9 5 5 10 5 4 9 5 6 11 6 3 9 6 1 7 4 6 10 6 2 8 5 5 10 6 3 9 6 4 10 6 4 10 5 6 11 6 5 11 6 5 11 6 6 12 6 6 12

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