Consider a deck of 30 cards. In this deck, 29 cards are common, and 1 is legendary. (If you use R code, show your R code) Let random variable X be the number of cards drawn until the legendary card is drawn. (e.g., if the first card you draw is the legendary, then x = 1. If you draw 4 normal cards and then a legendary, then x = 5) a) If you draw cards one at a time WITHOUT replacement from the deck, what is the PMF of X? b) What is the expected value of X, E[X]? c) What is the variance of X, Var(X)? d) If you draw cards one at a time WITH replacement from the deck, what is the PMF of X? (With replacement means that a card goes back into the deck, and the deck is shued, before another card is drawn) e) What is the name of the distribution of X when sampling WITH replacement. f) What is the expected value of X when sampling with replacement. g) What is the variance of X when sampling with replacement.