Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:

(a) the maximum value to appear in the two rolls;

(b) the minimum value to appear in the two rolls;

(c) the sum of the two rolls;

(d) the value of the first roll minus the value of the second roll?

Suppose that

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Answered by Aaron 2 years ago

**part (a)**

The random variable in this case is

X = maximum value to appear in the two rolls = {1,2,3,4,5,6}

so for instance, if I rolled a 1 and 2, the maximum would be 2 for that case.

**part (b)**

By the same reasoning in **part (a)**

X = {1,2,3,4,5,6}

in this case if I rolled a 1 and a 2, the minimum would be 1.

**part (c)**

The sum of the two rolls can take on the following values,

X = {2,3,4,5,6,7,8,9,10,11,12}

**part (d)**

suppose we rolled a 6 and then a 1 then X = 6-1 = 5

suppose we rolled a 1 and then a 6 then X = 1-6 = -5

so the min is -5 and max is 5, and we can get all values in between,

X = {-5,-4,-3,-2,-1,0,1,2,3,4,5}

It may be helpful to construct a table like the following,

1 | 2 | 3 | 4 | 5 | 6 | |

1 | (1,1,2,0) | (2,1,3,-1) | ||||

2 | (2,1,3,1) | (2,2,4,0) | ||||

3 | (3,1,4,2) | |||||

4 | ||||||

5 | ||||||

6 |

where the corresponding values are (min, max, sum, first die minus second) ie. I roll a 3 and then a 1 so I get (3,1,4,2)

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