CSE 240, Fall, 2013 Homework 4
Due, Thursday October 3. Can turn in class, at the beginning of class, or earlier in the mailbox labelled
Pless in Bryan Hall, room 509c.
Practice Problems:
1. Use a loop invariant to prove that the following program is corr
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Homework 8
Due: November 5, 2015
Question 1
(a) What is the probability that a five-card poker hand contains exactly one ace?
One Ace can be selected form 4 Aces in C (4,1) ways
The remaining 4 cards can be selected in C (48,4) ways
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Homework 7
Due: October 22, 2015
Question 3
3. A computer network consists of six computers. Each computer is directly connected to at
least one of the other computers. Show that there are at least two computers in the network
that
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Homework 7
Due: October 22, 2015
Question 2
2. How many license plates can be made using either three digits followed by three uppercase
English letters or three uppercase English letters followed by three digits.
A 3 decimal digit
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Homework 7
Due: October 22, 2015
Question 4
4. How many bit strings of length 12 contain
Bit strings can only contain 1s or 0s. The number of combinations of r distinct objects to be
chosen from n distinct objects is denoted by C(n,
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Homework 8
Due: November 5, 2015
Question 3
3. Show that if E and F are independent events, then
independent events.
E and F are also
Goal: P(E F) = P(E)P(F) and need to prove P( E F) = P( E)P( F)
P( E F) = P(EF)
de Morgan law
=1 P
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Homework 8
Due: November 12, 2015
Question 2
2. What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?
R: random variable that count the number of times a 6 appears when a fair die is flipped.
Di
Practice Final Exam 2010
Please write your name at the top of this page. There are no *trick* questions on this exam, but
approach each problem with an open mind. Please keep track of the time, and good luck.
1. (Very Short answer)
(a) Let A be the set cf
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Homework 8
Due: November 12, 2015
Question 1
1. Suppose that X and Y are random variables and that X and Y are nonnegative for all points in
a sample space S. Let Z be the random variable defined by Z(s) = max(X(s), Y (s) for all
el
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Homework 8
Due: November 5, 2015
Question 4
4. Find the smallest number of people you need to choose at random so that the probability that
at least one of them has a birthday today exceeds 1/2.
If n people are chosen at random, the
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Homework 8
Due: November 12, 2015
Question 4
4. Suppose that we roll a fair die until a 6 comes up.
(a) What is the probability that we roll the die n times?
X: number of times we roll the dice
1
p=
six sided dice
6
p(X = n) = (1-p)
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Homework 8
Due: November 12, 2015
Question 3
3. Provide an example that shows that the variance of the sum of two random variables is not
necessarily equal to the sum of their variances when the random variables are not independent.
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Homework 8
Due: November 24, 2015
Question 1
1. (a) Show that the relation R on a set A is reflexive if and only if the complementary relation
R is irreflexive.
A reflection R on a set A is reflective if (a,a) R for all a A
If (a,a
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Homework 10
Due: November 24, 2015
Question 3
3. Show that in a simple graph with at least two vertices there must be two vertices that have the
same degree.
Let R (x, y) be a graph with at least two vertices |v| 2. Each vertex has
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Homework 8
Due: November 24, 2015
Question 4
4. Show that the sum, over the set of people at a party, of the number of people a person has
shaken hands with, is even. Assume that no one shakes his or her own hand.
Assume that no one
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Homework 8
Due: November 5, 2015
Question 2
2. What is the probability of these events when we randomly select a permutation of the 26
lowercase letters of the English alphabet?
Q is the set of all permutations of 26 lower case lett
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Homework 7
Due: October 22, 2015
Question 1
How many strings of four decimal digits:
Decimal digit: integer between 0 and 9, meaning there are 10 choices total
Since every place is independent of the others there are 104 (the 4 come
Announcements
Quiz today
Exam Thursday!
You are allowed one 8.5 x 11 in cheat sheet of handwri;en notes
for the exam (front and back of 8.5 x 11 in paper)
Handwri;en means you must write them by hand, you may not print them out
Any a;empt to
Homework 1
Solutions
September 5, 2013
1. Let M be the proposition you cause a memory overow error.
Let P be the proposition you use pointers incorrectly.
Express each of the following statements using M, P , and logical connectives, for example, in an
ex
Homework 2
Solutions
September 17
1. Using (and citing) rules of inference and logical equivalence, Prove the following form of argument is
valid:
(P Q) R
R S
P S
There are many possible solutions. Here is one:
(P Q) R
Given
2.
RS
Given
3.
R S
Implies Rul
CSE 240, Fall, 2013 Homework 5
Due, Tues October 22. Can turn in class, at the beginning of class, or earlier in the mailbox labelled Pless
in Bryan Hall, room 509c.
Practice Problems:
1. Given two arbitrary sets A,B, prove that (A intersection B) union
(
Homework 7. CSE 240, Fall, 2013
Due, Tuesday November 24 at the beginning of class, or earlier in the mailbox labelled Pless in Bryan
Hall, room 509c. I do *not* accept homeworks e-mailed to me, so if you are leaving for Thanksgiving, turn
it in ahead of
Name:
1. (Very Short answer)
(a) (2 points) How many binary bit strings have exactly 3 1s and 8 0s, but no consecutive
1s?
(b) (2 points) For what values of k is
8
k
odd?
(c) (2 points) Let A = cfw_a, cfw_b, c, and B = cfw_d. Write down the powerset of A
Homework 6. CSE 240, Fall, 2013
Due, Thursday November 1. Can turn in at the beginning of class, or earlier in the mailbox labelled Pless
in Bryan Hall, room 509c.
Practice Problems:
1. Consider the function f : N N, dened by the mapping
f (x) = the numbe
CSE 240, Fall, 2013 Homework 2
Due, Tuesday September 17. Can turn in class, at the beginning of class, or earlier in the mailbox labelled
Pless in Bryan Hall, room 509c.
Practice Problems:
1. Consider the following english arguments. Dene propositions/pr
CSE 240, Fall, 2013 Homework 1
Due, Thursday September 5. Can turn in class, at the beginning of class, or earlier in the mailbox labelled
Pless in Bryan Hall, room 509c.
Practice Problems:
1. Which of the following are propositions:
(a) Blaise Pascal con
CSE 240, Fall, 2013 Homework 2
Due, Tuesday September 17. Can turn in class, at the beginning of class, or earlier in the mailbox labelled
Pless in Bryan Hall, room 509c.
Practice Problems:
1. Consider the following english arguments. Dene propositions/pr