STAT/MA 416
September 16, 2011
Problem Set 11
Name:
1a. Variance of an Indicator.
Suppose event
A
occurs with probability
p
, and
X
is an
indicator for
A
, i.e.,
X
= 1 if
A
occurs, or
X
= 0 otherwise. We already know
E
(
X
) =
p
.
Find Var(
X
).
1b. Butterflies.
Alice, Bob, and Charlotte are looking for butterflies. They look in three
separate parts of a field, so that their probabilities of success do not affect each other.
•
Alice finds 1 butterfly with probability 17%, and otherwise does not find one.
•
Bob finds 1 butterfly with probability 25%, and otherwise does not find one.
•
Charlotte finds 1 butterfly with probability 45%, and otherwise does not find one.
Let
X
be the number of butterflies that they catch altogether. Find the variance of
X
.
1
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2. Appetizers.
At a restaurant that sells appetizers:
•
8% of the appetizers cost $1 each,
•
20% of the appetizers cost $2 each,
•
32% of the appetizers cost $3 each,
•
40% of the appetizers cost $4 each.
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 Fall '08
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 Probability, Variance, Probability theory, white sock, Bob ﬁnds

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