AMS 311 (Fall, 2010)
Joe Mitchell
PROBABILITY THEORY
Homework Set # 4
Due at the beginning of class on Thursday, October 21, 2010.
Reminder: Show your reasoning!
Read: Ross, Chapter 4, Sections 4.5–4.9 (you can skip the Hypergeometric distribution (4.8.3) and the Zeta
distribution (4.8.4)), Sections 5.1–5.3.
SUBMIT ANY 4 OF THE 8 PROBLEMS BELOW. You should read and understand how
to do all 8 of them.
(1).
(25 points) The cdf of
X
is given by
F
(
x
) =
0
x <
−
4
3
/
10
−
4
≤
x <
1
7
/
10
1
≤
x <
4
1
x
≥
4
(a). (10 points) Find the variance and the standard deviation of
X
.
(b). (5 points) Find the variance of
Y
=
X
3
+ 12.
(c). (10 points) Find the cdf of
W
= 2
X
2
−
3.
(2).
(25 points) Suppose it takes at least 9 votes from a 12member jury to convict a defendant. Suppose
the probability that a juror votes a guilty person innocent is 0.2, whereas the probability that the juror votes
an innocent person guilty is 0.1. If each juror acts independently and if 65 percent of the defendants are
guilty, find the probability that the jury renders a correct decision.
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 Spring '08
 Tucker,A
 Variance, Probability theory, probability density function, CDF

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