A green die and a red die are rolled. The random variable X is the absolute value of the difference between the number of spots on the red die and green die.
The number of spots on the red die and green die is given in the sample space "S" below. The first value is the number of spots on the red die and the second value is the number of spots on the green die.
"S=\\begin{Bmatrix}\n (1,1) & (2,1)&(3,1)&(4,1)&(5,1)&(6,1) \\\\\n (1,2) & (2,2)&(3,2)&(4,2)&(5,2)&(6,2)\\\\\n(1,3)&(2,3)&(3,3)&(4,3)&(5,3)&(6,3)\\\\\n(1,4)&(2,4)&(3,4)&(4,4)&(5,4)&(6,4)\\\\\n(1,5)&(2,5)&(3,5)&(4,5)&(5,5)&(6,5)\\\\\n(1,6)&(2,6)&(3,6)&(4,6)&(5,6)&(6,6)\n\\end{Bmatrix}"
From the sample space, the absolute values of the difference between the number of spots on the red die and green die is given below.
"\\begin{Bmatrix}\n (0) & (1)&(2)&(3)&(4)&(5) \\\\\n (1) & (0)&(1)&(2)&(3)&(4)\\\\\n(2)&(1)&(0)&(1)&(2)&(3)\\\\\n(3)&(2)&(1)&(0)&(1)&(2)\\\\\n(4)&(3)&(2)&(1)&(0)&(1)\\\\\n(5)&(4)&(3)&(2)&(1)&(0)\n\\end{Bmatrix}"
Clearly,
there are 6 out out 36 values whose absolute difference is 0.
there are 10 out of 36 values whose absolute difference is 1.
there are 8 out of 36 values whose absolute difference is 2.
there are 6 out of 36 values whose absolute difference is 3.
there are 4 out of 36 values whose absolute difference is 4.
there are 2 out of 36 values whose absolute difference is 5.
Now, let the random variable "X"represent the absolute value of the difference between the number of spots on the red die and green die. The random variable "X" may take on the following values.
"x=0,1,2,3,4,5"
The probability distribution of "X" is given below.
"x" 0 1 2 3 4 5
"p(X=x)" "{6\\over36}" "{10\\over36}" "{8\\over36}" "{6\\over36}" "{4\\over36}" "2\\over36"
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