Final answer:
The probability mass function (PMF) of a random variable x corresponding to the absolute value of the difference between the results of two dice can be found by considering all possible outcomes and their probabilities. The PMF represents the probability of each possible value of x. The PMF for this random variable is 1/36, 2/36, 3/36, 4/36, 5/36, 6/36 for x values 0, 1, 2, 3, 4, 5 respectively.
Step-by-step explanation:
The probability mass function (PMF) of a random variable x corresponding to the absolute value of the difference between the results of two dice can be found by considering all possible outcomes and their probabilities.
Let's define the random variable x = |(result of first die) - (result of second die)|.
Since each die has 6 equally likely outcomes, the sample space for x consists of all integers from 0 to 5. To find the PMF, we need to determine the probability of each value of x.
Here is the PMF for the random variable x:
x: 0 1 2 3 4 5
P(x): 1/36 2/36 3/36 4/36 5/36 6/36