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Chapter 4 Homework key
2011/09/20
[Over 72 points]
403. [Chapter 4; 16 p.] (Definitions)
a)
[2 p.] What is a statistical experiment?
A natural or artificial process which produces, each time it is invoked, one
outcome out of a small set of possible outcomes, with a specific probability
distribution.
b)
[2 p.
] What is the “sample space” for a statistical experiment?
The sample space is the set of possible outcomes of the experiment.
c)
[2 p.
] What do we mean by “independent” statistical experiments?
If we do the same experiment twice in a row, the probabilities of the
different outcomes on the second try are not influenced by whatever
happened on the first try. If we carry out two different experiments, the
outcomes of one are not affected by whatever outcome resulted from the
other.
d)
[2 p.] Given an example of independent statistical experiments.
Rolling two dice, or rolling one die twice. Drawing two cards from a deck, or
two balls from an urn, with replacement (you replace the card or ball you
drew on the first try, and shuffle, before your second try.)
e)
[2 p.] Given an example of nonindependent statistical experiments.
The usual state lottery setup: you have a bunch of numbered balls in an urn,
you draw a sequence of balls without replacing the balls drawn. As you draw
each ball, the probabilities for the following draws change.
f)
[2 p.] For two sets A and B, define the Union
AB
The union of two sets is defined as the (larger) set of items that belong to
either A or B
(or both).
g)
[2 p.] For two sets A and B, define the Intersection
The intersection of two sets is defined as the (smaller) set of items that
belong to
both A and B
.
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h)
[2 p.] For set S and a subset A, define the Complement
c
Aor A
If A is a subset of S, then the complement of A with respect to S is defined
as the set of items that belong to S that are
not in A
.
414. [Ch. 4, 14 points] (Probability)
a)
[2 p.] You roll a die. What is the probability of rolling a 3 ?
1/6
b)
[2 p.] You roll a die. What is the probability of rolling a 2 or a 3 ?
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 Spring '09
 Business, Probability, Probability theory, Dice

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