Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution? constant symmetric positively skewed negatively skewed

The answer is: Symmetric.

symmetric

Step-by-step explanation:

First we find the sample space of rolling two dice:

(1, 1); (1, 2); (1, 3); (1, 4); (1, 5); (1, 6)

(2, 1); (2, 2); (2, 3); (2, 4); (2, 5); (2, 6)

(3, 1); (3, 2); (3, 3); (3, 4); (3, 5); (3, 6)

(4, 1); (4, 2); (4, 3); (4, 4); (4, 5); (4, 6)

(5, 1); (5, 2); (5, 3); (5, 4); (5, 5); (5, 6)

(6, 1); (6, 2); (6, 3); (6, 4); (6, 5); (6, 6)

We want the difference of the dice; this gives us the sample space

0; - 1; - 2; - 3; - 4; - 5;

1; 0; - 1; - 2; - 3; - 4;

2; 1; 0; - 1; - 2; - 3;

3; 2; 1; 0; - 1; - 2

4; 3; 2; 1; 0; - 2

5; 4; 3; 2; 1; 0

This makes the probability distribution:

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

Looking at the probabilities, we can see that the distribution is symmetric.