Solutions to Homework 12
FM 5001 Preparation for Financial Mathematics
Let X and Y be identically distributed PCRVs (piecewise constant random
variables). Assume Pr [X = 4] = 0.6 and Pr [X = 3] = 0.4. Let [1, 1]. Assume
E [XY ] = (E [Y ])2 + (V ar [Y ]).

FM 5001 NOTES 9/19/2012
1. Quiz
Problem 1. Use the prediction method to nd the derivative of the
function (cos(x)2 at x = /3. You are allowed to use the fact that
the derivative of cos(x) is sin(x), but you are not allowed to use the
chain rule directly.

FM 5001 NOTES 9/26/2012
1. Quiz
Problem 1. Draw a picture of the equation a(r + s) = ar + as, using
a = 2, r = (1, 1) and s = (2, 1).
Problem 2. Use the dot product to show that any vector that lies in
the plane 2x + y z = 1 is perpendicular to the vector

FM 5001 NOTES 9/12/2012
1. Review Questions from Last Week
For each of the following, determine the change of variables that
converts the relationship involving x, y into the relationship involving
u, v , or the other way around, depending on how the prob

FM 5001 NOTES 9/5/2012
1. Introduction
Each week, I will hand out notes to accompany my lectures for FM
5001. The purpose of this course is to prepare students for the mathematics that they will encounter in later FM courses. The main topics
that we will

FM 5001 Fall 2011, Final Exam
Ending time for in-person students: 8:00 pm on Wednesday 14 December 2011
Time for exam: 1.5 HOURS (ONE AND ONE HALF HOURS)
For PROCTORS of online students:
Email scan to: adams@math.umn.edu
Preferred FAX: 612-624-6702
Altern

FM 5001 Fall 2011, Midterm #2
Handout date: Wednesday 16 November 2011
Time for exam: ONE HOUR
For PROCTORS of online students:
Email scan to: adams@math.umn.edu
Preferred FAX: 612-624-6702
Alternate FAX: 612-626-2017
Exam must be received by 24 hours aft

FM 5001 Fall 2011, Midterm #1
Handout date: Wednesday 19 October 2011
Time for exam: ONE HOUR
For PROCTORS of online students:
Email scan to: adams@math.umn.edu
Preferred FAX: 612-624-6702
Alternate FAX: 612-626-2017
Exam must be received by 24 hours afte

FM 5001 NOTES 10/3/2012
1. Quiz
Problem 1. Consider the following two investment opportunities, showing the net prot under three possible outcomes: (10, 20, 30),(5, 10, 5)
Show that these do not oer the possibility of arbitrage, and determine
the price of