In: Advanced Math

**Please Answer 4.4.2: Do you see any problems with the
choice of hash functions in Exercise 4.4.1? What advice could you
give someone who was going to use a hash function of the form h ( x
) = ax + b mod 2 k ?**

Exercise 4.4.1:

Suppose our stream consists of the integers 3, 1, 4, 1, 5, 9, 2,6, 5. Our hash functions will all be of the form h (x) = ax+b mod 32 for some a and b. You should treat the result as a 5-bit binary integer. Determine the tail length for each stream element and the resulting estimate of the number of distinct elements if the hash function is:

(a) h(x) = 2x+ 1 mod 32.

(b) h(x) = 3x+ 7 mod 32.

(c) h(x) = 4x mod 32.

**4.4.2**

During the computational processes, it is obvious that this algorithm is quite sensitive to the hash function parameters. Some of the following advice may be useful for someone who is going to use the hash function of the form h ( x ) = ax + b mod 2^k. That is the parameters have to be odd numbers for the best result. Since when it is even number, whatever b is, the hash function does not generate good results.

When a is even, and b is odd, the hash function always returns odd numbers. That causes the binary value always ends by 1's, making the tail length is always equal to 0 as in case [a].

When a is even, and b is also even, the hashed value will be badly affected. For instance, in case [c] hashed values of 2 different elements become the same (both 1 and 9 have the same hashed value of 4). It revokes the primary rule of a hash function that is: "with different elements, the hash function is supposed to generate different values".

When using secure hash functions in an RSA signature, why do we
sign the hash Sign (H (m)) instead of taking the take the hash H
(Sign (m)) ?

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B
C...

What do you see as the main organizational problems that are likely
to be associated with implementation of a Global Standardization
Strategy? Please take one industrial as your case to explain your
answers explicitly in no less than 300 words

Exercise #6 (game theory and choice question)
PLEASE TYPE OUT ANSWER
We are presented with land use choices. Individuals are free to
choose their own development strategy based on the profit potential
of the development
.
a) Does either landowner have a
dominant strategy? (5 Points) A dominant strategy is what you are
going to do, knowing what they are going to do—this leads to the
Nash Equilibrium Explain how and what the dominant strategy is
(hint, there does...

A student wants to see if the correct answers to multiple choice
problems are evenly distributed. She heard a rumor that if you
don't know the answer, you should always pick C. In a
sample of 100 multiple-choice questions from prior tests and
quizzes, the distribution of correct answers are given in the table
below. In all of these questions, there were four options {A, B, C,
D}.
Correct Answers (n = 100)
A
B
C
D
Count
12
24 ...

A student wants to see if the correct answers to multiple choice
problems are evenly distributed. She heard a rumor that if you
don't know the answer, you should always pick C. In a
sample of 100 multiple-choice questions from prior tests and
quizzes, the distribution of correct answers are given in the table
below. In all of these questions, there were four options {A, B, C,
D}.
Correct Answers (n = 100)
A
B
C
D
Count
12
24 ...

A student wants to see if the correct answers to multiple choice
problems are evenly distributed. She heard a rumor that if you
don't know the answer, you should always pick C. In a
sample of 94 multiple-choice questions from prior tests and
quizzes, the distribution of correct answers are given in the table
below. In all of these questions, there were four options {A, B, C,
D}.
Correct Answers (n=94)n=94)
A
B
C
D
Count
22
13
27
32...

A student wants to see if the correct answers to multiple
choice problems are evenly distributed. She heard a rumor that if
you don't know the answer, you should always pick C. In a sample of
89 multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (?=89)
n
=
89
)
A B C D
Count...

Explain what the following notions mean for hash functions and
compare their strength. Please don’t copy the deﬁnitions from the
class slides, explain them with your own words.
• Collision Resistant
• Pre-image Resistant
• Second Pre-image Resistant

Do
you see any flaws with capitalism? If so,what are the flaws?

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