Consider the experiment of rolling a pair of dice. Using R, show how would you define a

random variable for the absolute value of the difference of the two rolls.

b) Using the above result, what is the probability that the two rolls differ by exactly 2? What is

the probability that the two rolls differ by at most 2? What is the probability that the two rolls

differ by at least 3? Use the Prob function as shown in the code samples.

c) Show the marginal distribution of the above random variable (using R).

d) Using R, add another random variable to the above probability space using a user defined

function. The random variable is TRUE if the two rolls differ by 2, and FALSE otherwise.

Making use of this random variable, what is the probability that the two rolls differ by 2? Show

also the marginal distribution for this random variable.