STATS:DATA+MODELS-W/DVD
4th Edition
ISBN: 9780321986498
Author: DeVeaux
Publisher: PEARSON
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Chapter 15, Problem 12E
a.
To determine
Construct a
b.
To determine
Find the expected amount of win.
c.
To determine
Explain how much money anyone should pay for this game.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
Chapter 15 Solutions
STATS:DATA+MODELS-W/DVD
Ch. 15.1 - 1. One of the authors took his minivan in for...Ch. 15.3 - 2. Suppose the time it takes a customer to get and...Ch. 15 - Prob. 1ECh. 15 - 2. Caffeinated A coffee shop tracks sales and has...Ch. 15 - 3. Oranges again What is the standard deviation...Ch. 15 - 4. Caffeinated again What is the standard...Ch. 15 - 5. Salary An employer pays a mean salary for a...Ch. 15 - 6. Golf scores A golfer keeps track of his score...Ch. 15 - 13. Battery The life span of a calculator battery...Ch. 15 - 14. Ketchup An automatic filling machine in a...
Ch. 15 - 15. Expected value Find the expected value of each...Ch. 15 - 16. Expected value Find the expected value of each...Ch. 15 - 17. Pick a card, any card You draw a card from a...Ch. 15 - 18. You bet! You roll a fair die. If it comes up a...Ch. 15 - 19. Kids A couple plans to have children until...Ch. 15 - 20. Carnival A carnival game offers a $100 cash...Ch. 15 - 21. Software A small software company bids on two...Ch. 15 - Prob. 16ECh. 15 - Prob. 17ECh. 15 - Prob. 18ECh. 15 - Prob. 19ECh. 15 - 26. The die Find the standard deviation of the...Ch. 15 - Prob. 21ECh. 15 - Prob. 22ECh. 15 - Prob. 23ECh. 15 - 30. Red lights A commuter must pass through five...Ch. 15 - 31. Defects A consumer organization inspecting new...Ch. 15 - 32. Insurance An insurance policy costs $100 and...Ch. 15 - Prob. 27ECh. 15 - Day trading An option to buy a stock is priced at...Ch. 15 - Prob. 29ECh. 15 - 36. Contracts Your company bids for two contracts....Ch. 15 - Prob. 31ECh. 15 - Prob. 32ECh. 15 - Prob. 33ECh. 15 - Prob. 34ECh. 15 - Random variables Given independent random...Ch. 15 - 42. Random variables Given independent random...Ch. 15 - Prob. 37ECh. 15 - 44. Garden A company selling vegetable seeds in...Ch. 15 - Prob. 39ECh. 15 - Stop! Find the mean and standard deviation of the...Ch. 15 - Tickets A delivery company’s trucks occasionally...Ch. 15 - Donations Organizers of a televised fundraiser...Ch. 15 - 49. Fire! An insurance company estimates that it...Ch. 15 - Prob. 45ECh. 15 - 52. Pets The American Veterinary Association...Ch. 15 - Prob. 47ECh. 15 - More pets You’re thinking about getting two dogs...Ch. 15 - 55. Medley In the 4 × 100 medley relay event, four...Ch. 15 - Prob. 50ECh. 15 - Prob. 51ECh. 15 - 58. Bike sale The bicycle shop in Exercise 56 will...Ch. 15 - 59. Coffee and doughnuts At a certain coffee shop,...Ch. 15 - Prob. 54E
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