HW#7, Due 04/27
AMS 311 Probability Theory (Spring 2011)
Read: Ross, Chapter 6, Sections 6.4–6.5. Chapter 7, Section 7.5 and the handout on ratin
maze problems.
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.
You do not need to evaluate
arithmetic expressions or integrals, if they are fully specified.
For example,
you may leave
in this form.
(1) (30 points) Consider the maze shown below. There are three cells (Cell 1, Cell 2, and Cell 3)
and two deadly (quite permanent) outcomes (Death By Poison, and the dreaded Death By
Guillotine). A rat is initially placed in cell 1. When the rat enters Cell i, he wanders around
within the cell for X
i
minutes, where X
i
is uniformly distributed between
i
and
i
2
, and then he
exits the cell by picking one of the doors at random (e.g., if there are 3 doors, he picks each with
probability 1/3).
(a). Find the probability that the rat dies by poison. (Recall that he starts in Cell 1.)
(b). What is the expected number of minutes that the rat lives?
(c). What is the probability the rat visits Cell 2 before he dies?
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 Spring '08
 Tucker,A
 Probability theory, probability density function, joint probability density, lowest homework grade

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