I need a step by step walk through of how to do these problems. This is a practice exam. I know how to start many of the problems, but not quite how to finish. I need help learning the actual processes.

Use R Studio and R coding for calculations and graphing.

Final Exam Please, write clearly and justify all your steps, to get proper credit for your work. You are allowed to use the textbook and your hand calculator. You are supposed to use the statistical tables from the book to solve some of the problems. (1) [4.5 Pts] From an ordinary deck of 52 playing cards, cards are drawn successively at random and without replacement. Compute: (a) The probability that the first five cards drawn from the deck contain at most 1 spade. (b) The probability that the first five cards drawn from the deck contain exactly 2 spades. (c) The probability that the third spade appears on the sixth draw. (2) [2 Pts] On average 8 calls per hours are received at the front desk of the Math department. Assuming that the number of calls per hour can be modelled as a Poisson r.v., find the probability that at any given hour, more than 6 calls are received. (3) [6 Pts] Let the joint p.d.f. of the discrete r.v. X and Y, denoted by f(x, y), be given by X 2 0.15 0.2 0.25 0.4 (a) Calculate the marginal densities. Are X and Y are independent? (b) Compute the means and variances. (c) Compute the correlation coefficient. Are X and Y positively correlated? negatively corre- lated? uncorrelated? (4) [4.5 Pts] Let X be a continuous r.v. with p.d.f. f(x) = 2x, 0 10). (b) Compute the probability P(|X 16|