550.171 Discrete Mathematics - midterm #1 supplement SOLUTIONS/SKETCHSpring 2007 1. The following are all separate questions. (a) Ten boys are to be seated in a circular arrangement of chairs. The teacher can place the boys in any of the chairs, but she w
550.171 Discrete Mathematics Homework Assignment #12 will not be collected From the text: Section 35 / 35.13 Section 36 / 36.11, 36.12, 36.13 Section 37 / 37.1, 37.3 (b,d only) 12.1. Consider the following system of congruences: 11x 4 (mod 14) 2x 9 (mod 1
550.171 Discrete Mathematics Homework Assignment #11 Thursday, April 26 From the text: Section 34 / 34.1, 34.2, 34.6 , 34.9 Section 35 / 35.1, 35.2, 35.11, 35.15 Section 36 / 36.1, 36.2
Spring 2007
this problem is optional/bonus: you do not have to do thi
550.171 Discrete Mathematics - Spring 2005 Name
Midterm #2
1. [15 pt] Prove: if G is a connected graph with n vertices and n edges (n 3), then G contains a cycle.
2. Let A and B be sets. (a) [3 pts] Briey explain what is meant by f : A ! B .
(b) [7 pts] S
550.171 Discrete Mathematics - Spring 2005 Name
Midterm #1
1. (a) [5 pt] State a careful denition of what it means for a positive integer to be composite.
(b) [10 pt] Recall from the rst day of class that if p is a prime such that 2p 1 is also prime, then
550.171 Discrete Mathematics - Fall 2004
Midterm #2
Name Print your name on each sheet; No Calculators; No notes; Leave your ID on your desk. 1. Let A = cfw_a, b, c, d and R = (a, cfw_b, c, d), (b, cfw_a, c, d), (c, cfw_a, b, d), (d, cfw_a, b, c) . (a) [2
550.171 Discrete Mathematics - Fall 2004
Midterm #1
Name Print your name on each sheet; No Calculators; No notes; Leave your ID on your desk. 1. Short Answer. (a) [6 pt] State the denition of a relation on a set A.
(b) [7 pt] Let A cfw_1, 2, 3. How many r
550.111 Statistical Analysis I - Spring 2007 Name
Midterm #3 version A
1. Suppose a random sample of size n measurements is taken from a normally distributed population with unknown mean and unknown standard deviation . The sample mean and sample standard
550.111 Statistical Analysis I - Spring 2007
Midterm #3 version A solution/sketch
1. Suppose a random sample of size n measurements is taken from a normally distributed population with unknown mean and unknown standard deviation . The sample mean and samp
550.111 Statistical Analysis I - Spring 2007 Name
Midterm #2 version B
1. Suppose Y is a Poisson random variable with parameter = 2.56. (a) [5 pt] Write down the formula for P (Y = x), and please be sure to mention the values x for which the formula is va
550.111 Statistical Analysis I - Fall 2007
Midterm #2 solutions
1. (a) Answer in 20 words or less: What is a random variable? A random variable is a function that assigns a numerical value to each outcome of an experiment. (b) A mouse is put into compartm
550.446 Risk Management Analysis and Hedging, Spring 2010 TA Section 03 Peter C.L. Lin [email protected]
1
7.19
Homework Review
The delta with respect to the st factor is 0.21 5 + 0.26 (3) + 0.32 (1) + 0.35 2 + 0.36 5 + 0.36 7 + 0.36 8 = 7.85. Similarly,
550.446 Risk Management Analysis and Hedging, Spring 2010 TA Section 02 Peter C.L. Lin [email protected]
1
4.16
Homework Review
The investors overall return is 1.08 0.92 1.12 0.88 1 = 0.0207 or 2.07% for the four years.
6.16
The price, delta, gamma, vega,
550.446 Risk Management Analysis and Hedging, Spring 2010 TA Section 01 Peter C.L. Lin [email protected]
1
Plan for TA Section
Go through homework, especially those further problems. Provide some interesting materials related to the lectures. Answer ques
550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010 TA Section 03 Peter C.L. Lin [email protected]
1
Homework Review
29.11
To calculate the convexity adjustment for the ve-year rate dene the price of a ve year bond, as a func
550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010 TA Section 02 Peter C.L. Lin [email protected]
1
Homework Review
28.22
The quoted futures price corresponds to a forward rate is 8% per annum with quarterly compounding and
550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010 TA Section 01 Peter C.L. Lin [email protected]
1
What will you learn in 445?
We will focus on two main topics: (1) Interest Rate Models, and (2) Credit Derivatives. The math