You are given two fair six-sided dice.One of them has the usual six sides (numbers 1-6).The other dice is unusual in that it has the following six sides: 1, 1, 1, 3, 3, 5.A random variable g is defined as the largest number from a single role of both dice.For example, if the two dice roll a 2 and a 5 respectively, the random variable g has the outcome 5.

a.Describe the sample set G of possible outcomes for random variable g.

b.Write the probability distribution for the random variable g.

Hint: A matrix or tree diagram or table of possible outcomes is useful in computing the probabilities.

c.Compute the probabilities of these three events: (i) P(g = 4), (ii) P(g 5), and(iii) P(g is an even number).

d.Calculate the expected value E(g) (the mean).

e.Compute the variance and standard deviation of random variable g.