a)Consider the experiment of rolling three dice. Using R, show how would you use a user-defined function to define a random variable that is the mean of the three rolls rounded to the nearest integer.

b)Using the above result, what is the probability that the random variable equals 3? What is the probability that the random variable takes a value of at most 3? What is the probability that the random variable takes on a value of 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 first random variable is even and FALSE otherwise. What is the probability that the first random variable is even? Show the marginal distribution for the 2nd random variable.