please solve using R studio and show script

(a) Find the sample space for this experiment in R. (Hint: convert to data.frame) (b) Let X be the number of movies from the 1970's chosen by a random member. Find the PMF of X. (Hint: By reordering the movies, we can assume that the movies from the 1970's are the first four in the list) (c) Find the expected value of X. (d) Find Var(X ) and ox. Problem 2: A metal fabricating plant currently has five major pieces under contract, each with a deadline for completion. Let X be the number of pieces completed by their deadlines. Suppose that X is a random variable with PMF p(x) given by 1 2 3 5 p(x) 0.05 0.1 0.15 0.25 0.35 0.1 (a) Compute the expected value and variance of X. (Hint: Use either the sum or weighted . mean commands) (b) Let Y be the remaining production budget for the company. The company starts with a budget of $20.000 but each piece completed reduces the budget by $1,000. Find the expected value and variance of Y. (Hint: Write Y as a linear transformation of _X ) (c) For each piece completed by the deadline, the plant receives a bonus of $15,000. Find the expected value and variance of the total bonus amount