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Math 132a: Stochastic Processes
Final Exam
(3/22/03)
Write your name and student ID number in the upper righthand corner of this sheet and write your initials
on each page of your exam.
Each problem is worth the same number of points. You
must
justify or defend your answer for each problem.
1.
Suppose that you ﬂip a fair coin four times. Let
A
1
be the event that the ﬁrst coin ﬂips 1 and 2 agree, let
A
2
be the event that coin ﬂips 2 and 3 agree, let
A
3
be the event that coin ﬂips 3 and 4 agree, and let
A
4
be the event that coin ﬂips 4 and 1 agree. Are these four events pairwise independent? Are they
mutually independent?
2.
In the computer game Minesweeper, you have a ﬁeld of squares, some of which contain mines. When
you step on a square which is not a mine, it tells you the number of neighboring mines. Suppose
that at the beginning each square in the game has a
1
4
chance of being a mine and that all of these
probabilities are independent. Suppose that later in the game you have three squares
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This note was uploaded on 05/19/2009 for the course MATH 150A taught by Professor Kuperberg during the Spring '03 term at UC Davis.
 Spring '03
 Kuperberg

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