Question

The sample space of tossing two dice is given. Let x = the sum of the two dice. Find the probability distribution for the random variable x. (List the values of x and their corresponding probabilities.) (1.1) (2.1) (3,1) (4,1) (5,1) (6,1)

(1.2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1.6) (2,6) (3,6) (4,6) (5,6) (6,6)

Answer 1

To find the probability distribution for x, we list the values of x and their corresponding probabilities. The probabilities are: x = 2 (1/36), x = 3 (2/36), x = 4 (3/36), x = 5 (4/36), x = 6 (5/36), x = 7 (6/36).

Step-by-step explanation:

The random variable x represents the sum of the two dice. To find the probability distribution for x, we need to list the values of x and their corresponding probabilities.

1. x = 2: There is only one way to get a sum of 2 (1,1), so the probability is 1/36.
2. x = 3: There are two ways to get a sum of 3 (1,2) and (2,1), so the probability is 2/36.
3. x = 4: There are three ways to get a sum of 4 (1,3), (2,2), and (3,1), so the probability is 3/36.
4. x = 5: There are four ways to get a sum of 5 (1,4), (2,3), (3,2), and (4,1), so the probability is 4/36.
5. x = 6: There are five ways to get a sum of 6 (1,5), (2,4), (3,3), (4,2), and (5,1), so the probability is 5/36.
6. x = 7: There are six ways to get a sum of 7 (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), so the probability is 6/36.