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?

Question

Adam Bradley · Accepted Answer

Let us suppose that a die is rolled twice. The maximum of two rolls is also random variable (not so trivial). What are the possible values?We assume that die consists of numbers {1, 2, 3, 4, 5, 6} therefore there are 36 combinations that can occur.Since for every k∈{1,2,3,4,5,6} ordered pair (k, k) can occur, maximum value can possibly achieve values of{1,2,3, 4,5, 6}.Let us observe the minimal value to appear in the two rolls. Since (k, k) can obviously occur in two rolls (where k &amp;amp; {1, 2,3, 4, 5, 6}.) minimal value can take values of {1, 2, 3, 4,5, 6}.In each roll numbers from 1 up to 6 can occur, therefore it is obvious that smallest sum is 2 and the largest is 12. It is trivial to see that every number inbetween can occur. Therefore the answer is:{2,3,4,5,6,7,8,9, 10,11, 12}.It remains to answer what are the possible values when we consider first roll minus the second roll. As we have mentioned before in every roll numbers from {1, 2, 3, 4, 5, 6} can occur. Therefore it is obvious that the wanted set of numbers is:{-5,-4, -3, -2, -1,0,1,2, 3, 4,5}.Hence, we are done.Result:We have: {1, 2,3, 4, 5, 6} for the a, b part, set {2, 3, 4,5, 6, 7,8, 9, 10, 11, 12} for the c part and finally {-5, -4, -3, -2, -1,0, 1, 2,3, 4,5} for the d part.

Open question

Answer & Explanation

New Questions in College Statistics