22M:150:001 Quiz 7
Duration of quiz: 10 minutes.
30th November 2012
Calculators, books or formula sheets are NOT allowed.
Name: SOLUTIONS
1. Suppose E and F are two events in a sample space. Further, suppose P (E ) = 1 ,
3
2
P (F ) = 1 and P (E |F ) = 5 .
Selected Answers to HW 7
October 8, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 6.1
1. a) 5850.
b) 343.
4. 72.
8. 1
Some Answers/Solutions to HW 1
September 6, 2012
Note: There may be more than one possible solution for some of the questions. Also,
I have copied some of the solutions from the solution manual without checking them so
watch out for typos.
Section 1.1
4a)
Student: Yu Cheng (Jade)
Math 475
Homework #1
January 20, 2010
Section 1.8
Exercise 1:
Show that an -by- chessboard has a perfect cover by dominoes if and only if at least one of
and is even.
Answer:
Step 1. Suppose one of and is even and the other one i
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. Albert R. Meyer and Prof. Ronitt Rubinfeld
Course Notes, Week 11
November 16
revised November 23, 2005, 700 minutes
Generating Functions
Generating funct
Week 9-10: Recurrence Relations and Generating
Functions
March 31, 2015
1 Some number sequences
An infinite sequence (or just a sequence for short) is an ordered array
a0 , a 1 , a 2 , . . . , a n , . . .
of countably many real or complex numbers, and is
Homework 7 Solutions
1. In walking from work back home at the end of the day, Grigor must travel six
blocks east and four blocks south. How many possible routes can he take, assuming
that he goes either east or south at each intersection? How many routes
Student: Yu Cheng (Jade)
Math 475
Homework #3
March 1, 2010
Section 4.6
Exercise 36-a
Let be a set of elements. How many different relations on are there?
Answer:
On set with elements, we have the following facts.
Number of two different element pairs
Num
Selected Hints/Answers to HW 8
October 16, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 6.2
4. a) 5.
b) 13.
7. Look
Selected Hints/Answers to HW 9
October 30, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 6.2
29. R(2, n) is the minim
Selected Answers to HW 10
November 3, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 6.5
41.
52
7
45
7
38
7
31
7
24
7
22M:150:001 Quiz 6
Duration of quiz: 10 minutes.
14th November 2012
Calculators, books or formula sheets are NOT allowed.
Name: SOLUTIONS
1. Suppose ve cards are chosen from a regular pack of 52 cards. What is the probability
that they contain the two of
22M:150:001 Quiz 5
Duration of quiz: 10 minutes.
24th October 2012
Calculators, books or formula sheets are NOT allowed.
Name: SOLUTIONS
1. Does a sequence of 9 distinct real numbers always have an increasing OR decreasing
subsequence of 4 numbers?
(5 poi
22M:150:001 Quiz 4
Duration of quiz: 10 minutes.
10th October 2012
Calculators, books or formula sheets are NOT allowed.
Name: SOLUTIONS
1. Prove that:
12 + 32 + (2n 1)2 =
n(2n 1)(2n + 1)
.
3
(5 points.)
Solution: We have to prove the identity for all nat
22M:150:001 Quiz 3
Duration of quiz: 10 minutes.
19th September 2012
Calculators, books or formula sheets are NOT allowed.
Name:
1. Find the greatest common divisor of 2987 and 4669.
(5 points.)
Well use the Euclidean Algorithm to determine the greatest c
Selected Answers to HW 14
November 26, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 8.6
2. 1000 450 622 30 + 111 + 1
Selected Answers to HW 13
December 4, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 8.2
3
4. a) an = 5 (2)n + 12 3n .
Selected Answers to HW 12
November 26, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 7.2
1
31. a) 32 .
b) 0.495 .
c)
Selected Answers to HW 11
November 3, 2012
Note:
1. There is a possibility of typos; in case you notice one, let me know.
2. These are just the answers; you must show work in your homework/quiz to get full credit.
Section 7.2
23.
1
.
4
25.
3
.
8
26. Yes.
Jeff Maxey
Operation: Internet Freedom
Censorship of the Internet, also known as filtering, has been a rising controversy across
the world for over the past decade. The Internet is a public common that is used all across the
world. Vast amounts of people