Question

2. Let us define a new variable Y = the sum of two dice. Complete both...

2. Let us define a new variable Y = the sum of two dice. Complete both the probability and cumulative probability tables for Y. (Hint: First think about what values Y can take on, and then notice rolling a die produces 6 outcomes but rolling two dice produces 36 outcomes. The following table can help you enumerate all 36 outcomes and find out what is the associated Y value for each outcome.) 1 2 3 4 5 6 1 Y=2 . . . . . 2 . . . . . 3 . . . . . . 4 . . . . . . 5 . . . . . . 6 . . . . . . Can someone help show how to calculate the cumulative probability for this question?

Math   Statistics-And-Probability   
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Answer #1

Solution:-) The total possible outcomes of two random dice.

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)
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)

So, Y can take value from 2,3,4,5,..................12.

y P(Y=y) Cumulative prob.
2 1/36 1/36
3 2/.36 1/36+2/36 = 3/36
4 3/36 6/36
5 4/36 10/36
6 5/36 15/36
7 6/36 21/36
8 5/36 26/36
9 4/36 30/36
10 3/36 33/36
11 2/36 35/36
12 1/36 36/36 =1
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