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Statistics 408
Homework Set III
Winter 2004
1. The physician claims that the probability that a patient has a viral infection is 95%.
What does this statement mean? Is this a property of the individual?
2. In the Monte Hall Game, explain why the strategy to switch has probability 2/3rds of
winning.
3. Define the symbols P[A| B], P[B | A], P[A & B], P[A or B], and P[not A]. Provide
examples of each.
4. In the “Birthday Paradox” we calculate the probability of the event that there is “no
match.” Explain how to do this and why we do it.
5. Provide examples to illustrate when seemingly rare events may are not uncommon.
(Hint: There are four separate circumstances described in lecture. Explain each, and
provide an example.)
6. What is a retrospective study of past events? What can you learn from such a study?
What is an appropriate "control" to help evaluate the result of such a study?
7. What is a prospective study of future events? What can you learn from such a study?
What is an appropriate "control" to help evaluate the result of such a study?
8. What do we mean when we say two events A and B are independent? What data
would support such a conclusion? Give an example of two dependent events.
9. Suppose you are told that 18% of a population has been involved in "shoplifting."
What proportion (guess) of the population is a “teenager who has been involved in
shoplifting?" Explain your guess.
10. Explain why Herbie, in the Goal, should be first in line and also the desired
arrangement of the other scouts. State this as a principle, and find another
application.
11. Are there circumstances when the definition of probability, presented in class, will
require a different operational definition?
12. Distinguish between a stochastic system and a deterministic system. Why do we need
to know the difference between the two?
13. How would we assess the quality of a weather forecaster? Assume the weather
forecaster may make assertions such as “it will rain with probability .4?”
14. What is a “stable system?”