Concept explainers
(a)
The expected pay off of an infinite series.
(a)
Answer to Problem 67RE
The value of
Explanation of Solution
Given information:
Toss a fair coin which the heads and tails are equally likely. When it comes up head on winning the dollar hence the game is over as soon as it comes up for the tails.
Formula used:
The Probability of occurring the tail in first chance,
Calculation:
Let the event when head appear be H and when tail appears being T.
Probability of occurring the tail in first chance,
Similarly,
Payoff when tail occur in first time
Payoff when tail occur in second time
Therefore,
Conclusion:
The value of
(b)
The value of the series
(b)
Answer to Problem 67RE
The value is
Explanation of Solution
Given:
The series is
Formula used:
Maclaurin series is used.
Calculation:
Maclaurin series generated by function
Differentiating the above expression
Therefore,
Conclusion:
The value is
(c)
The value of the series
(c)
Answer to Problem 67RE
The value is
Explanation of Solution
Given information:
The series is
Formula used:
Multiplication is used.
Calculation:
Multiplying the above series by
Therefore,
Conclusion:
The value is
(d)
The expected payoff of the game.
(d)
Answer to Problem 67RE
The expected payoff is $1
Explanation of Solution
Given information:
The series is
Formula used:
Division is done.
Calculation:
If
Since,
Therefore expected payoff is $1
Conclusion:
The expected payoff is $1
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning