1) Consider a player endowed with 3 USD starting a game in which at every play she/he may win or loose 1 USD with probabilitypand(1p)respectively. Let and denote the player endowment withX. a. Derive the probability distribution ofXafter 3 plays. Construct a graphical representation of this discrete random variable. b. What is the mean and the variance of the player endowment. c. What is the probability that the player will lose all her/his endowment after 3 plays? And that she/he will double it?