Consider a game which involves rollingthreedice. Write theR codefor the following.

Using therollDiefunction from theproblibrary, setup the sample space for this experiment with the probability space.

Code: rolldie(3, nsides = 6, makespace = TRUE)

a)The sum of the rolls is greater than 10.

b)All the three rolls are identical.

c)Only two of the three rolls are identical.

d)None of the three rolls are identical.

e)Only two of the three rolls are identical given that the sum of the rolls is greater than 10.

f)Add a random variable to the sample space for the sum of the rolls. Show the marginal distribution of this random variable. Using this random variable, what is the probability that the sum of the rolls is greater than 10.

g)Add a random variable to the sample space for determining whether all the rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that all the rolls are identical.

h)Add a random variable to the sample space for determining if only two out of the three rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that only two out of the three are identical.

i)Add a random variable to the sample space for determining if none of the three rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that none of the three are identical.