Question

Consider an experiment of tossing two fair dice and noting the outcome on each die. The whole sample space consists of 36 elements. Now, with each of these 36 elements associate values of two random variables, X and Y, such that X≡ sum of the outcomes on the two dice, Y ≡ |difference of the outcomes on the two dice|. Construct joint probability mass function.

Answer 1

The joint probability mass function based on the given experiment is as seen in the attached file.

How to construct a joint probability mass function?

The whole sample space consists of 36 elements, i.e.,

Ω = {ω_ij = (i, j) : i, j = 1, ....6}

Now, with each of these 36 elements associate values of two random variables, X₁ and X₂, such that;

X₁ ≡ sum of the outcomes on the two dice.

X₂ ≡ |difference of the outcomes on the two dice|

That is;

X(ω_ij) = X₁(ω_ij) + X₂(ω_ij) = (i + j, |i - j|) i, j = 1, 2, ...., 6

Then, the bivariate rv X = (X₁, X₂) has the following joint probability mass

function (empty cells mean that the pmf is equal to zero at the relevant values of the rvs).

The joint probability mass function is seen in the attached file.

Read more about  joint probability mass function at; brainly.com/question/14002798

#SPJ1