Consider a game which involves rolling three dice. Write the R code for

the following.

Using the rollDie function from the prob library, setup the sample space

for this experiment with the probability space.For each of the following

scenarios from a) through e), show the corresponding outcomes and

the probability of that event. The sample outputs for b) are shown asexample.

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

b) All the three rolls are identical.

Sample Output for outcomes:

X1 X2 X3 probs

1 1 1 1 0.00463

44 2 2 2 0.00463

87 3 3 3 0.00463

130 4 4 4 0.00463

173 5 5 5 0.00463

216 6 6 6 0.00463

Sample Output for probability: 0.02778

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.

Please take a look the question above and please provide the R code detail as much as possible.