Question

Consider the experiment of tossing 2 fair dice independently and let X denote their difference (first...

Consider the experiment of tossing 2 fair dice independently and let X denote their difference (first die minus second die).
(a) what is the range of X?
(b) find probability that X=-1.
(c) find the expected value and variance of X. Hint: let X1, X2 denote #s on the two dice and write X=X1-X2
Math   Statistics-And-Probability   
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Answer #1
(1,1)=0 (1,2)=-1 (1,3)=-2 (1,4)=-3 (1,5)=-4 (1,6)=-5
(2,1)=1 (2,2)=0 (2,3)=-1 (2,4)=-2 (2,5)=-3 (2,6)=-4
(3,1)=2 (3,2)=1 (3,3)=0 (3,4)=-1 (3,5)=-2 (3,6)=-3
(4,1)=3 (4,2)=2 (4,3)=1 (4,4)=0 (4,5)=-1 (4,6)=-2
(5,1)=4 (5,2)=3 (5,3)=2 (5,4)=1 (5,5)=0 (5,6)=-1
(6,1)=5 (6,2)=4 (6,3)=3 (6,4)=2 (6,5)=1 (6,6)=0

a) range = -5,-4,-3,-2,-1,0,1,2,3,4,5

b) P( X =-1) = 5/36 = 0.1389

X -5 -4 -3 -2 -1 0 1 2 3 4 5
P(X) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

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