CK-12 Probability and Statistics - Advanced

7.5. Sums and Differences of Independent Random Variables http://www.ck12.org

At this time, there are two ways that you can create probability distributions from data. Sometimes previously
collected data, relative to the random variable that you are studying, can serve as a probability distribution. This
was the case with the data received from the local cable company in Fort McMurray. In addition to this method, a
simulation is also a good way to create an approximate probability distribution. A probability distribution can also
be constructed from basic principles and assumptions by using the rules of theoretical probability. The following
examples will lead to the understanding of these rules of theoretical probability.

Example:

Create a table that shows all the possible outcomes when two die are rolled simultaneously. (Hint: There are 36
possible outcomes.)

2 nd Die

1 2 3 4 5 6

1 1 , 1 1 , 2 1 , 3 1 , 4 1 , 5 1 , 6

2 2 , 1 2 , 2 2 , 3 2 , 4 2 , 5 2 , 6

3 3 , 1 3 , 2 3 , 3 3 , 4 3 , 5 3 , 6 1 stDie

4 4 , 1 4 , 2 4 , 3 4 , 4 4 , 5 4 , 6

5 5 , 1 5 , 2 5 , 3 5 , 4 5 , 5 5 , 6

6 6 , 1 6 , 2 6 , 3 6 , 4 6 , 5 6 , 6

This table of possible outcomes when two die are rolled simultaneously can now be used to construct other proba-
bility distributions. The first table will display the sum of the two die and the second will represent the larger of the
two numbers.

TABLE7.7:

Sum of Two Die,x Probability,p

2 1 / 36

3 2 / 36

4 3 / 36

5 4 / 36

6 5 / 36

7 6 / 36

8 5 / 36

9 4 / 36

10 3 / 36

11 2 / 36

12 1 / 36

Total 1

TABLE7.8:

Larger Number,x Probability,p

1 1 / 36

2 3 / 36

3 5 / 36

4 7 / 36

5 9 / 36

6 11 / 36