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HW#4, Solutions
AMS 311 Probability Theory (Spring
2011)
Part 1 (10 points):
PRINT
your name and StonyBrook ID (
Last, First, #ID
) on the top on your work
sheet. Staple your HW if more than 1 pages.
Part 2: Problems (90 points)
Write down your work step by step to get full score.
(1).
For a given defendant, the number of votes for guilty follows a binomial distribution.
So , (which means at least 9 jurors vote
an innocent person “guilty”).
Similarly,
The event that the jury renders a wrong decision could be decomposed to disjoint events: voting
a guilty person innocent, and voting an innocent person guilty. That is:
, and we know P(G)=0.65.
So P(E)=1P(E)=
(2).
Let X
a
, X
b
, X
c
be the error number in this 7page article if it is typed by Alan, Bob or Cathy,
respectively. The best model is Poisson Process. That is X
a
~Poisson(), =3*7=21; X
b
~Poisson(),
=4.2*7=29.4; X
c
~Poisson(), =2.1*7=14.7.
Let X be the error number in this 7page article. Using the law of total probability,
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This note was uploaded on 05/09/2011 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Tucker,A

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