solve using R or R studio

1. Assume that X, the value an unfair die, has the following probability mass function. 6 2 1- a)6 (a) What values for a are possible? (b) Find the mean = EaX and the variance 2-Vira(X). (c) Let X be the average of 100 dice rolls find the mean EaX and the variance Vara(X) d) For independent observations, x-(x,r2,..., ^100), of this random variable from a given value of a, give a, the method of moments estimate 1. Assume that X, the value an unfair die, has the following probability mass function. 6 2 1- a)6 (a) What values for a are possible? (b) Find the mean = EaX and the variance 2-Vira(X). (c) Let X be the average of 100 dice rolls find the mean EaX and the variance Vara(X) d) For independent observations, x-(x,r2,..., ^100), of this random variable from a given value of a, give a, the method of moments estimate