Math 362 - Review #1 - Fall 2002
Introduction
to Probability Theory
Review for Test # 1
Close all books and notebooks and ask yourselves the following questions.
- Experiments, sample space, outcomes, events
- What is an experiment? Give an example.
- Given an experiment, how do you find its sample space?
- What is an outcome?
- Can a sample space contain an infinite number of outcomes? Why or why not?
- Is there a difference between an outcome and an event? Give examples.
- Set theory
- In a word problem, how would you recognize that you have to find
- the union
- the intersection
of two events?
- In a word problem, how would you recognize that you have to find the
complement of one event?
- What are the properties of the union, the intersection and the complement?
- What does it mean that two events are mutually exclusive?
- Definition of probability
- What are the 3 axioms of probability?
- What is the probability of
- What is the formula for the probability of the union of two events?
- Can you explain what this formula tells you in terms of Venn diagrams?
- What is the formula for the probability of the union of three events?
- What does it mean that two events are equally likely?
- Random variables
- What is a random variable? Give an example.
- What is the difference between a discrete and a continuous random variable? Give examples.
- What is a Bernoulli random variable?
- What is a binomial random variable?
- What is the p.m.f. of a random variable? What kind of information does it give you?
What are its properties? Give an example.
- What is the p.d.f. of a random variable? What kind of information does it give you?
What are its properties? Give an example.
- What is the difference between a p.d.f. and a p.m.f. ?
- What is the c.d.f. of a random variable? What kind of information does it give you?
What are its properties?
- How would you be able to tell whether a given function could or could not be
- a p.m.f.?
- a p.d.f.?
- a c.d.f.?
- How would you find the c.d.f. of a random variable if you were given
- The graph of its p.m.f. or p.d.f.?
- A formula for its p.m.f. or p.d.f.?
- How is the mean of a random variable defined? Give formulas.
- How would you estimate the mean of a random variable from the graph of its p.d.f. or
p.m.f.?
- Can a random variable have more than one mean?
- What is a median of the distribution of a random variable? How is it defined?
How can there be more than one median? Give examples.
- How do you calculate the expectation of a function of a random variable?
- Sketch the p.m.f. of a finite random variable. Label the axes and use this information
to find the expectation and a median of this random variable.
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