A=9 B=8

9130 AM Wed Jan 26 '5' 61% I Assignment 4 Please note that most questions are personalized, where a is the last digit of your student number and b is the third last digit of your student number. For example, if your student number is 0012345, then a = 5 and b = 3. MATH104AO/MGMT290AO Assignment #4 Following Unit 2 in the manual. 1. [2 points] A certain random variable 1' takes the values 3 + a, 2, 1 and 2 b with respective probabilities 0.1, 0.2, 0.3, 0.4. Find the mean and the standard deviation of :L'. 2. [4 points] A casino owner designs a game in which a regular deck of 52 cards (without the two jokers) is shuied and a gambler is allowed to select a card at random. If he selects a K (i.e., a King) he wins $10. If he selects a Q (i.e., a Queen) he wins $(5 + a). If he selects a J (i.e., a Jack) he wins $1. If he selects any other card he loses $(2 + b). a. Find the probability that the gambler wins $(5 +a) in a game. Interpret your answer in terms of a relative frequency. . If we use 1: to denote the amount of money (in dollars) the gambler could win in a game, nd the probability distribution of the random variable 3:. . Find the mean and standard deviation of the random variable 11:. . Interpret the answer the preceding question. 3. [4 points] Based on a Comcast survey, (20+a)% of adults in a certain country will watch prime- time TV online. (This means that there is a (0.2 + 0.01 X a) probability that a randomly selected adult will watch prime-time TV online). Assume that 7 + b adults are randomly selected. Let .'L' be the random variable that counts the number of selected adults who watch prime-time TV online. (a) Does 1 yield a binomial probability distribution? Why? (b) Find the probability that non of the selected adults watch prime-time TV online. (c) Find the probability that exactly 2 of the selected adults watch prime-time TV online. (d) Find the probability that at least one of the selected adults watches primetime TV online. (e) Use formulas p. = rip and a = m to nd the mean and standard deviation of r. (f) Interpret your answer to the preceding