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Two six-sided dice, one red and one white, will be rolled. List the possible values for each of the following random variables. (Enter your answers as comma-separated lists.)

Respuesta :

Answer:

(a) x = sum of the two numbers showing

       = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)

(b)  y = difference between the number on the red die and the number on the white die (red − white)

       = (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)

(c) w = largest number showing

       = 1, 2, 3, 4, 5, 6

Step-by-step explanation:

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The possible values of the variables are:

  • x ∈ {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
  • y ∈ {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
  • z ∈ {1, 2, 3, 4, 5, 6}

How to find the possible values for the random variables?

Here we have 3 random variables, let's define them:

  • x = sum of the values.
  • y = difference of the values (red - white).
  • z = largest value.

For the first variable we are just adding the values on the dice, the smallest possible value is when both dice give the outcome 1,

1 + 1 = 2

The largest value is when the two dice give the outcome 6.

6 + 6 = 12

And we will also have all the integer values in between:

x ∈ {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

For the second variable we do the same thing, let's find the extremes.

The smallest possible value is when the red dice outcome is a 1, and the white dice outcome is a 6.

1 - 6 = -5

The largest possible value is when the red dice outcome is a 6, and the white dice outcome is a 1.

6 - 1 = 5

Then the possible values of that variable are:

y ∈ {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

For the third variable the possible values are the same ones that in each single dice (because we just look at the two outcomes and we select the larger one) so the possible values are:

z ∈ {1, 2, 3, 4, 5, 6}

If you want to learn more about random variables, you can read:

https://brainly.com/question/15246027

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