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What is the answer for 4.21 a? "Which of E[X] or E[Y] do you think is larger? Why?"

What is the answer for 4.21 a? "Which of E[X] or E[Y] do you think is larger? Why?"

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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What is the answer for 4.21 a? "Which of E[X] or E[Y] do you think is larger? Why?"

10 1 35b<3.5 b23.5 calculate the probability mass function of X. 4.20. A gambling book recommends the following "winning strategy" for the game of roulette: Bet $1 on red. If red appears (which has 18. probability), then take the $1 profit and quit. If red does not 38' 20 appear and you lose this bet (which has probability of occurring), 38 make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit. Let X denote your winnings when you quit. a. Find P{X>0}. b. Are you convinced that the strategy is indeed a "winning" strategy? Explain your answer! c. Find E[X]. 4.21. Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. a. Which of E[X] or E[Y] do you think is larger? Why? b. Compute E[X] and E[Y]. Page 280 / 848 4.22. Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and (b) i = 3. Also, show in both cases that this number is maximized when p = 1 =20 4.23. You have $1000, and a certain commodity presently sells for $2 per ounce. Suppose that after one week the commodity will sell for +
Transcribed Image Text:10 1 35b<3.5 b23.5 calculate the probability mass function of X. 4.20. A gambling book recommends the following "winning strategy" for the game of roulette: Bet $1 on red. If red appears (which has 18. probability), then take the $1 profit and quit. If red does not 38' 20 appear and you lose this bet (which has probability of occurring), 38 make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit. Let X denote your winnings when you quit. a. Find P{X>0}. b. Are you convinced that the strategy is indeed a "winning" strategy? Explain your answer! c. Find E[X]. 4.21. Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. a. Which of E[X] or E[Y] do you think is larger? Why? b. Compute E[X] and E[Y]. Page 280 / 848 4.22. Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and (b) i = 3. Also, show in both cases that this number is maximized when p = 1 =20 4.23. You have $1000, and a certain commodity presently sells for $2 per ounce. Suppose that after one week the commodity will sell for +
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