Math 350 - Homework 1 - Solutions
1. Interpret the following Matlab expressions:
(a) r = rand; a = (r <= 1/2)
The random variable a takes only the values 1 or 0. It is 1 if and only if r is less than
Math 350 Fall 2012 - Homework 5
Due 10/05/2012
1. Read text, Chapter 3, pages 101 to 107. (There are interesting topics I have skipped from Chapter
2; I plan to return to them later.)
2. Approximate B
Math 350 Fall 2012 - Homework 8
Due 11/9/2012
Here are some general geometric denitions and background facts related to the problems below.
(All but the last problem are to be solved by hand.) The n-d
Math 350 Fall 2012 - Homework 10
Due 11/30/2012
The Ising model. The Ising model originated in statistical physics as a mathematical model for ferromagnetism,
but it has found much broader applicabili
Math 350 Fall 2012 - Homework 9
Due 11/19/2012
The hard-core model. (This example is adapted from Finite Markov Chains and Algorithmic Applications, by
Olle Hggstrm, London Mathematical Society, Stude
Math 350 Fall 2012 - Homework 6
Due 10/12/2012
Denitions for problem 1. Problem 1 deals with the class structure of a Markov chain. It is sometimes
possible to break a Markov chain into smaller pieces
Math 350 Fall 2012 - Homework 11
Due 12/07/2012
Simulated annealing and the traveling salesman problem. See pages 139-146 of textbook. The traveling salesman
problem is a widely studied model optimiza
Math 350 Fall 2012 - Homework 7
Due date: 10/29/2012
The beta distribution. The beta distribution is a family of continuous probability distributions dened on the
interval [0, 1], parametrized by two
Math 350 - Homework 2
Due 2/05/2010
1. (Text, problem 7, page 35.) If X and Y have a joint probability density function given by
f (x, y) = 2e(x+2y)
for x and y in (0, ), nd the probability P (X < Y )
Math 350 - Homework 3
Due 2/12/2010
1. (Text, problem 25, page 37.) The bus will arrive at a time that is uniformly distributed between 8 and
8 : 30 A.M. If we arrive at 8 A.M., what is the probabilit
Math 350 - Homework 1
Due 1/29/2010
The probabilistic experiment consisting of picking a random number between 0 and 1 with the uniform
probability distribution over the interval [0, 1] is approximate
Math 350 - Homework 4
Due 2/19/2010
1. (Text, problem1, page 46.) If x0 = 5 and
xn = 3xn1 (mod 150)
nd x1 , . . . , x10 .
2. (Text, problem 6, page 47.) This problem refers to the integral
x(1 + x2 )2
Math 350 - Midterm test - Solutions
1. If X and Y have a joint probability density function given by
f (x, y ) = 2e(x+2y)
for x and y in (0, ), nd the probability P (X < Y ).
y
2e(x+2y) dx dy
P (X < Y
Math 350 - Homework 5
Due 2/26/2010
1. (Text, problem 4, page 63.) A deck of 100 cardsnumbered 1, 2, . . . , 100is shued (i.e., a random
permutation is applied to the cards in the deck) and then turne
Math 350 - Homework 4
Due 9/28/2012
1. Read text, chapter 2, pages 51 - 69.
2. (Problem 8, chapter 2, page 95) The sphere S n1 is dened to be the hypersurface in Rn consisting
of points x = (x1 , . .
Math 350 Fall 2012 - Homework 3
Due 9/21/2012
1. Browse the Notes on Random Variables:
http:/www.math.wustl.edu/~feres/Math350Fall2012/Notes_on_random_variables.pdf
(You can nd a link to it on the Cou
Math 350 - Homework 4
Solutions
1. Read text, chapter 2, pages 51 - 69.
2. (Problem 8, chapter 2, page 95) The sphere S n1 is dened to be the hypersurface in Rn consisting
of points x = (x1 , . . . ,
Math 350 Fall 2012 - Homework 3
Solutions
1. Browse the Notes on Random Variables:
http:/www.math.wustl.edu/~feres/Math350Fall2012/Notes_on_random_variables.pdf
(You can nd a link to it on the Course
Math 350 - Homework 2 - Solutions
1. Read text, section 1.2 (pages 10 - 27.)
2. (Text, problem 8, page 44) Random walk with drift. Use a biased coin to simulate a random walk of
30 steps on the line.
Math 350 - Homework 1 - Solutions
1. Interpret the following Matlab expressions:
(a) r = rand; a = (r <= 1/2)
The random variable a takes only the values 1 or 0. It is 1 if and only if r is less than
Math 350 Fall 2012 - Homework 5
Solutions
1. Read text, Chapter 3, pages 101 to 107. (There are interesting topics I have skipped from Chapter
2; I plan to return to them later.)
2. Approximate Browni
Math 350 Fall 2012 - Homework 6
Solutions
Denitions for problem 1. Problem 1 deals with the class structure of a Markov chain. It is sometimes
possible to break a Markov chain into smaller pieces that
Math 350 Fall 2012 - Homework 10
Solutions
The Ising model. The Ising model originated in statistical physics as a mathematical model for ferromagnetism,
but it has found much broader applicability, i
Math 350 Fall 2012 - Homework 9
Solutions
The hard-core model. (This example is adapted from Finite Markov Chains and Algorithmic Applications, by
Olle Hggstrm, London Mathematical Society, Student Te
Math 350 Fall 2012 - Homework 8
Solutions
Here are some general geometric denitions and background facts related to the problems below.
(All but the last problem are to be solved by hand.) The n-dimen
Math 350 Fall 2012 - Homework 7
Solutions
The beta distribution. The beta distribution is a family of continuous probability distributions dened on the
interval [0, 1], parametrized by two positive pa
Math 350 Fall 2012 - Homework 11
Solutions
Simulated annealing and the traveling salesman problem. See pages 139-146 of textbook. The traveling salesman
problem is a widely studied model optimization
Math 350 - Homework 1
Due 9/07/2012
The probabilistic experiment consisting of picking a random number between 0 and 1 with the uniform
probability distribution over the interval [0, 1] is approximate
Math 350 - Homework 2
Due 9/14/2012
1. Read text, section 1.2 (pages 10 - 27.)
2. (Text, problem 8, page 44) Random walk with drift. Use a biased coin to simulate a random walk of
30 steps on the line
Math 350 - Midterm test - March 5, 2010
1. If X and Y have a joint probability density function given by
f (x, y) = 2e(x+2y)
for x and y in (0, ), nd the probability P (X < Y ).
2. Let X be a binomial