What is the answer for 4.21 a? "Which of E[X] or E[Y] do you think is larger? Why?"
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 6E
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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
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0618968-6b5a-406b-a92d-661b061825b7%2F06060e46-c76d-4c32-80ac-d189475f002d%2Ff6xtlap_processed.jpeg&w=3840&q=75)
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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