STAT/MA 416
September 23, 2011
Problem Set 14
Name:
1. Winnings and Losing.
Suppose that a person wins a game of chance with probability
0
.
40, and loses otherwise. If he wins, he earns 5 dollars, and if he loses, then he loses 4
dollars. Assume that he plays ten games independently. Let
X
denote the number of games
that he wins. [Hint: His gain or loss is 5
X
+ (

4)(10

X
) = 9
X

40, since he loses 10

X
games.]
(a.) What is his expected gain or loss (altogether) during the ten games?
(b.) What is the variance of his gain or loss (altogether) during the ten games?
(c.) What is the probability that he wins $32 or more during the ten games?
1
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One out of every eight calls to your house is a telemarketer. Assume
that the likelihood of telemarketers is independent from call to call. Let
X
denote the
number of telemarketers during the next three calls.
(a.) What is the mass of
X
?
(b.) Draw a picture of the mass of
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 Fall '08
 Staff
 Probability, Probability theory, binomial random variable, Binomial random variables, dining hall

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