QUESTION 1

1. Imagine you just had an election between two candidates: Abby and Tanya. There are 10,000 voters. After you count each vote, you calculate the percent of the vote Abby has so far. (In other words, you record the percent of counted voters who voted for Abby after one vote is counted, then after a second vote is counted, then after a third vote is counted, etc.)

   If you graphed Abby's percent of support after each vote counted, with the number of votes counted on the x-axis, how should the graph look? (Keep in mind the law of large numbers.)

   		Volatile on the left and smoothly upward or downward sloping (depending on if she wins or loses) on the right.
   		Smoothly upward or downward sloping (depending on if she wins or loses) on the left and volatile on the right.
   		Volatile on the left and flat on the right.
   		Flat on the left and volatile on the right.

20 points   

QUESTION 2

1. Randy and Monica have three sons. They love their sons but they would like to have a daughter. Randy convinces Monica to have a fourth child because, according to the law of large numbers, the child is likely to be female. Is Randy correct?

   		No, because Randy’s succumbing to the gambler’s fallacy.
   		No, because Randy’s succumbing to the hot hand fallacy.
   		Yes, because as the number of trials increases the empirical average should approach the theoretical average.
   		No, because they are more likely to have a so

When 2.50 moles of N₂(g) is heated in a piston having a constant pressure of 1.75 atm from 0.00 ^oC to 125 ^oC, calculate the work, expressed in J, associated with this process. Interpret the sign of your answer.

What type of directional valve is used to control the forward and reverse of a double-acting hydraulic piston?
a) 3 way/ 2 position
b) 4 way/ 2 position
c) 4 way/ 3 position

and why?

Design a complete program that asks the user to enter a series of 20 numbers. The program should store the numbers in an array and then display each of the following data:

I. The lowest number in the array

II. The highest number in the array

III. The total of the numbers in the array

IV. The average of the numbers in the array

*PYTHON NOT PSUEDOCODE AND FLOW CHART!!!!*

Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15. not sure with current solution posted, personally it wasn't clear step by step working. I get lost with some values that he gets ( not sure where he gets them )

here's the question:

To get full marks for the following questions you need to convert the question from words to a mathematical expression (i.e. use mathematical notation), defining your random variables where necessary, and using correct probability statements.

Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15.

1. (a) [2 marks] What IQ score distinguishes the highest 10%?

2. (b) [3 marks] What is the probability that a randomly selected person has an IQ score between

   91 and 118?

3. (c) [2 marks] Suppose people with IQ scores above 125 are eligible to join a high-IQ club. Show that approximately 4.78% of people have an IQ score high enough to be admitted to this particular club.

4. (d) [4 marks] Let X be the number of people in a random sample of 25 who have an IQ score high enough to join the high-IQ club. What probability distribution does X follow? Justify your answer.

5. (e) [2 marks] Using the probability distribution from part (d), find the probability that at least 2 people in the random sample of 25 have IQ scores high enough to join the high-IQ club.

6. (f) [3 marks] Let L be the amount of time (in minutes) it takes a randomly selected applicant to complete an IQ test. Suppose L follows a uniform distribution from 30 to 60. What is the probability that the applicant will finish the test in less than 45 minutes?

The Mall Street Journal is considering offering a new service which will send news articles to readers by email. Their market research indicates that there are two types of potential users, impecunious students and high-level executives. Let x be the number of articles that a user requests per year. The executives have an inverse demand function P E( x ) = 100 − x and the students have an inverse demand function P U( x ) = 80 − x . (Prices are measured in cents.) The Journal has a zero marginal cost of sending articles via email.

Suppose that the journal cannot observe which type any given user is. The journal continues to o§er two packages. Suppose that it offers one package which allows up to 80 articles (intended for students) and one package that allows up to 100 articles (intended for professors). What is the highest price that students will be willing to pay for the 80-article package? What is the highest price that the journal can charge for the 100-article package if it offers the 80-article packages at the highest price the students are willing to pay? In this situation, what is the consumer surplus obtained by a professor?

Assume that the number of executives in the population equals the number of students. Let (Xe,Te) be the profit maximizing "executive package", where Xe is the number of articles the executive can access at a Total charge of Te, and (Xu,Tu) be the profit maximizing "student package", where Xu is the number of articles the student can access at a total charge of Tu. Is Xe=100? Is Xu=80? Explain. Derive the values of Xe,Te,Xu,Tu.

One file java program that will simulate a game of Rock, Paper, Scissors. One of the two players will be the computer. The program will start by asking how many winning rounds are needed to win the game. Each round will consist of you asking the user to pick between rock, paper, and scissors. Internally you will get the computers choice by using a random number generator. Rock beats Scissors, Paper beats Rock, and Scissors beats Paper. You will report the win, loss, or tie and continue with another round. Repeating until either the user or the computer has won the correct number of times first. Please output what the user and computers choice is each time and give a running score total as the game goes on.

Output should look like:

Welcome to my game of Rock, Paper, Scissors!
How many winning rounds are needed for victory? :3

Round# 1
Enter 0=rock, 1=paper, 2=scissors:0

Human : Rock Computer : Rock
Draw, try again
Total Score: Human 0 Computer 0

Round# 2
Enter 0=rock, 1=paper, 2=scissors:1

Human : Paper Computer : Rock
Human wins this round
Total Score: Human 1 Computer 0

Round# 3
Enter 0=rock, 1=paper, 2=scissors:2

Human : Scissors Computer : Paper
Human wins this round
Total Score: Human 2 Computer 0

Round# 4
Enter 0=rock, 1=paper, 2=scissors:0

Human : Rock Computer : Rock
Draw, try again
Total Score: Human 2 Computer 0

Round# 5
Enter 0=rock, 1=paper, 2=scissors:0

Human : Rock Computer : Scissors
Human wins this round
Total Score: Human 3 Computer 0

It took 5 rounds, but you won!
Goodbye, play again sometime

Part II: What is security and security in the NIST standard (HD tasks)

The importance of defining security is that, if you don’t know what security means, then you never know whether you have achieved your security goal or not in real applications. Let’s work through the strict definitions of security under different attack assumptions gradually and then see how the NIST standard applies the definitions (implicitly). From a high-level-point of view, any private key cryptosystem Π (for example, AES) can be defined as a collection of three algorithms (Gen, Enc, Dec) over the message space M (the symbol means “belong to”):

Gen (key-generation algorithm): an algorithm produces the key k;

Enc (encryption algorithm): takes key k and message mM as input; outputs

ciphertext c (c C, C is the ciphertext space);

Dec (decryption algorithm): takes key k and ciphertext c as input; outputs m or “error”.

The correctness of Enc and Dec indicates that, for all mM and k output by Gen, Deck(Enck(m)) = m.

First, let’s consider the case of security definition under Ciphertext-Only-Attack (in short as COA, and COA is also called eavesdropping attack). It starts with a game between the adversary A and a Challenger C. The Challenger C is in charge of Π, so he can do encryptions and decryptions. And all the technique details of Π are known to the Adversary A but the key, A wants to learn the information about plaintext as much as he can through interaction with C. In the case of COA, the interactions can be captured by this game: COA-Game:

The attacker A chooses two message m0 and m1 of equal length, say n bits, and sends them both to C.

The challenger C tosses a coin and determines a random bit b (say for example, “head” as “1” and “tail” as “0”). Then he set cb = Enck(mb) and sends cb to A.

The attacker tries his best to work out b and outputs another bit b’. If b’ = b, then A wins this game.

We say the cryptosystem Π= (Gen, Enc, Dec) is perfect indistinguishable under the COA attack if the probability that A wins the above COA-Game is ½, formally, we denote this as

Prob(ACOA(b’= b)) = ½.

1. Prove that the one-time-pad (OTP) is perfect secure under COA attack, i.e., the challenge ciphertext cb could come from either m0 or m1 with equal probability from the best of the attacker’s knowledge.

The definition of perfect indistinguishable is too strong to be applied in real life, and so does the OTP. So, we need to relax it to a more realistic definition, and it is called computational   indistinguishable   in   the   literature.   Informally,   computational indistinguishable means that we allow a tiny chance (for example, ½^128) that the attacker A can tell the cb is from m0 or m1 better than random guessing. That is, the cryptosystem Π= (Gen, Enc, Dec) is computational indistinguishable under the COA attack if the probability that A wins the above COA-Game is ½ + neg. Formally, we denote it as

Prob(ACOA(b’= b)) = ½ + neg.,

where neg. is a negligible probability (say for example, ½^128). In short, we write computational indistinguishable under the COA-Game as COA-IND.

QUESTION 4 (2 + 1 + 2 + 1 + 4 =10 marks)

It is believed that cities tend to attract workers that are better educated. A sample of 610 people were classified by their highest education level (Primary and secondary school, Undergraduate and Postgraduate degree) and whether a person is working in a city or a town. The following information was obtained:

• Primary and secondary school: 89 people in total finished primary and secondary school as their highest qualification; 51 people completed their primary and secondary education and work in a city.

• Undergraduate degree: 349 people in total completed undergraduate degree as their highest qualification; 220 people completed their undergraduate degree and work in a city.

• Postgraduate degree: 172 people in total completed postgraduate degree as their highest qualification; 116 people completed their postgraduate education degree and work in a city.

1. What is the probability that a person, who has completed primary and secondary school as their highest qualification, works in a town. Show your working.

2. Let the variable Education represent the highest education level and the variable Working Status represent whether a person is working in a city or a town. Name the dependent variable.

3. We would like to investigate if there is an association between the level of education and whether a person is working in a city or town. What type of test would you conduct and why?

4. State the appropriate hypotheses statements of the test above.

5. Assume that we carry out the test above at the 1% level of significance. The test statistic value is 4.75. State the decision rule, decision, and conclusion in the context of this question. (Hint: You can use a critical value approach OR p-value approach to derive your decision)

Some researchers argue that revenue sharing is like socialism in that it removes the incentive to outperform rivals. Do you agree with this statement? Why or why not?