Answer to Question #180077 in Statistics and Probability for Laiba shah

Question

10.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?

Answer 1

(a) A die is rolled twice.

The different faces of a die are 1,2,3,4,5,6

So, the number of possible outcomes when a die is rolled twice = 6^2 = 36

List of possible outcomes:

The maximum value to appear on the dice in two rolls can be any of the set of values: 1, if ‘1’ appears both times maximum value will be 1, 2, 3, 4, 5, 6

Let X be the random variable representing the maximum value to appear in the two rolls. Then X takes values from the set {1,2,3,4,5,6}

(b) The minimum value to appear on the dice in two rolls can be any of the values: 1, 2, 3, 4, 5, 6 (if ‘6’ appears both times then minimum value will be 6) as seen from the list of possible outcomes

Let X be the random variable representing the minimum value to appear in the two rolls. Then X takes values from the set {1,2,3,4,5,6}

(c)

The sum of the values in the two rolls can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 as seen from the above table.

Let X be the random variable representing the sum of the values in the two rolls.

X can take values from the set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(d)

The value of the first roll minus the value of the second roll can be any of the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 as seen from the above table.

Let X be the random variable representing the value of the first roll minus the value of the second roll.

X can take values from the set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}