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

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

S
40 points

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
SnakeOil

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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)

R
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