Question

A balanced die is tossed twice. Let X and Y denote the smaller and larger of the two faces. Find the joint probability mass function (PMF) of X and Y.

Answer 1

Each cell in the table represents the probability of obtaining a specific pair of X=x and Y=y, and for a fair die, all 36 outcomes are equally likely.

Step-by-step explanation:

The joint probability mass function (PMF) of X and Y can be found by considering all possible outcomes of tossing two balanced dice. Let's denote the smallest face as X and the largest face as Y. There are 36 possible outcomes when two dice are tossed, as there are 6 possible outcomes for each die.

To calculate the PMF, we need to count how many outcomes have X=x and Y=y for each possible pair of x and y. For example, if X=2 and Y=4, there is only one outcome where the first die shows 2 and the second die shows 4 (2,4).

By considering all 36 possible outcomes, we can construct a table showing the joint PMF of X and Y. Each cell in the table represents the probability of obtaining a specific pair of X=x and Y=y. For a fair die, all 36 outcomes are equally likely, so each cell in the table will have a probability of 1/36.