D4.1

1. Let us use the variable X to represent number of dots from tossing a fair die.

Given the following probability table for X,

x 1 2 3 4 5 6

P(X= x) 1/6 1/6 1/6 1/6 1/6 1/6

Complete the following table for X, which is termed cumulative probability.

For example: P(X<=2)= P(X=1) + P(X=2).

x 1 2 3 4 5 6

P(X<=x)

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 noticerolling 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