Have you ever wondered why people act the way they do on Black Friday or on the 4th of July? Or why wealthy people and nations have less children than poorer ones? Or why we buy flowers or a card for a loved one knowing that it will end up in the garbage later?

(a) Suppose that the random variable T is exponentially distributed with parameter > > 0 and hence T has the (cumulative) distribution func- tion Fr(t ) = 1 1 -ext t > 0 and 0 > 0 if the distribution function of X is given by r 0 find an expression for P(X > a+b | X >a). [4 marks] By considering the ratio P(X > a+b | X > a) P(X > b) show that in the case 3 = 2, the distribution of X does not possess the memoryless property. [4 marks] For which values of the parameters 3 and 0, if any, does the Weibull distribution possess the memoryless property? [1 mark] (c) Suppose that the lifetime Y (in years) of a specific electrical component follows the Weibull distribution with parameters 3 = 2 and 0 = 1. Treating b as a fixed constant, define a function g(a) by g ( a ) = P ( Y > atb | Y > a ) . Give your interpretation of the shape of the graph of g(a). [4 marks]BIG DATA GETS PERSONAL: BEHAVIORAL TARGETING Ever get the feeling somebody is trailing you on the Such code can match people's identities with their Web, watching your every click: Do you wonder why Web browsing activities on an unprecedented scale you start seeing display ads and pop-ups just after and can even track a user's arrival on a page if the you've been searching the Web for a car a dress, or button is never clicked. cosmetic product? Well, you're right your behavior is In separate research, the Journal examined what being tracked, and you are being targeted on the Web happens when people logged in to roughly 70 popu- as you move from site to site in order to expose you lar Websites that request a login and found that more to certain "targeted" ads. It's Big Data's dark side. than a quarter of the time, the sites passed along a Individual web sites and companies whose bust- user's real name email address or other personal ness is identifying and tracking Internet users for details to third-party companies advertisers and marketers are collecting data on Online advertising titans like Google, Microsoft. your every online move, Google, which handles and Yahoo are all looking for ways to monetize more than 3 5 billion Web searches each day, knows their huge collections of online behavioral data. more about you than your mother does, Many of the While search engine marketing is arguably the most tracking tools gather incredibly paronal informa- effective form of advertising in history, untargeted ton such as age, gender, race, income, marital status banner display ad marketing is highly inefficient health concerns (health topics you search on), TV because it displays ads to everyone regardless of shows and movies viewed, magazines and newspa their interests. As a result. these firms cannot charge pors road, and books purchased A $31 billion dollar much for display ads. However, by tracking the online ad industry is driving this intense data col- online movements of 245 million U.S. Internet users, lection, Facebook, which maintains detailed data on they can develop a very clear picture of who you are, over 1 billion users, employs its Like button to follow and use that information to show you ads that might users around the Web even if you log off Its social be of interest to you. This would make the marketing networking site is one giant tracking system that process more efficient, and more profitable for all remembers what you like, what your friends like, the parties involved, and whatever you reveal on your Wall. (See the chap- You're also being tracked closely when you use ter-ending case study ) Plus, Google's social network. your mobile phone to access the Internet, visit your ing tool knows about your friendships on Gmail, Facebook page, get Twitter feeds, watch video, and the places you go on maps, and how you spend listen to music. The mobile Web is working hard to your time on the more than two million websites in keep track of your whenabouts, locations, habits, Google's and network. It is able to gather this inforing- and friends in the hope of selling you even more tion even though relatively few people use Plus for products and services their social network. New technologies found on smartphones cin While tracking firms claim the information they Identify where you are located within a few yards gather is anonymous, this is true in name only, Performing routing actions using your smart phone Scholars have shown that with just a fow pieces makes it possible to locate you throughout the day. of information, such as age, grinder, zip code, and to report this information to corporate databases, marital status, specific individuals can be easily retain and analyze the information, and then sell it Identified. Moreover, tracking firms combine their to advertisers. Most of the popular apps report your online data with data they purchase from offline location. Law enforcement agencies certainly have firms who track retail store purchases of virtually all an interest in knowing the whemahouts of criminals Americans Here, personal names and other identi- and suspects, There are, of course, many times when Hers are used you would like to report your location wither auto- Use of real identities across the Web is going matically or on your command. If you were injured, mainstream at a rapid clip. A Wall Street Journal for instance, you might like your cell phone to be examination of nearly 1 000 top Websites found that able to automatically report your location to authori- 75% now include code from social networks, such ties, or if you were in a restaurant, you might want as Facebook's "Like" or Twitter's "Tweet' buttons to notify your friends where you are and what youare doing, But what about occasions when you don't earned $2.2 billion from its mobile ads. Smartphone want anyone to know where you are, least of all apps that provide location-based services are also advertisers and marketers? sources of personal, private location information Location data gathered from cell phones has based on the smartphone GPS capability. extraordinary commercial value because advertising Expect those eyes to follow your movements even companies can send you highly targeted advertise- more in the future as behavioral targeting becomes ments, coupons, and flash bargains, based on where even more precise. New software is being developed you are located. This technology is the foundation for to help advertisers track users across devices by many location-based services, which include smart- establishing cross-screen identities, That means that phone maps and charts, shopping apps, and social companies will be able to serve ads to your mobile apps that you can use to let your friends know where phone based on what they learned about you from you are and what you are doing, Revenues from the surfing the Web on your PC. global location-based services market are projected to Sources: Claire Cain Miller, The Plus in Google Plus? It's Mostly reach reach $10.3 billion in 2015, according to Gartner. for Google," New York Times, February 14, 2014, Elizabeth Dwoskin, Both Apple's Phone and Google's Android "Internet Users Tap Tech Tools That Protect Them From Prying phones collect personal, private location data, and Eyes," Wall Street Journal, March 23, 2014: Claire Cain Miller and Somni Sengupta, "Selling Secrets of Phone Users to Advertisers," both firms are building massive databases that can New York Times, October 5, 2013, Natasha Singer, Their Apps Track pinpoint your location. Advertising firms pay Apple You, Will Congress Track Them?' The New York Tum, January S and Google for that information and for distributing 2013, Spencer E Ante, "Online Ads Can Now Follow Your Home," The Wall Street Journal, April 29, 2013, Jennifer Valentino-Devries their mobile ads, and they are becoming increas and Jeremy Singer, "They Know What You're Shopping For," The Wall ingly important sources of revenue. In 2012, Google Street Journal, December 7, 2013: CASE STUDY QUESTIONS 1. Why is behavioral tracking such an important 3. What would happen if there were no behavioral ethical dilemma today? Identify the stakeholders tracking on the Internet? and interest groups in favor of and opposed to behavioral tracking, 2. How do businesses benefit from behavioral track- ing? Do people benefit? Explain your answer.General guidelines for this project: Formulate a statistical question that you would like to answer from data already published on the internet or through an experiment, sample, survey, or study. Do not choose a topic that may cause any physical pain or harm to yourself or anyone else. Keep your design simple, See below for examples. Carefully consider what data collection design you will use to answer your question, Examples: o If you are conducting an experiment, how can you include an element of randomization? Will your experiment be blind? If so, will it be single- or double-blind? If not, why is blinding not possible? How many trials will you conduct? If you are conducting a survey or study, can you randomly select the participants or objects? Is your question unbiased? o If you are selecting published data, how will you verify that it is reliable? Define the variable of interest State the inference procedure(s) you will use. Get approval for your proposal from your teacher before collecting data Show all your work to receive full credit. In the project work: Verify that the conditions for the inference are satisfied, State the name of the inference procedure. Calculate and state the appropriate statistic(s) Conduct the inference Summarize your findings. Type your work into this document or print the document and show your work by hand. Submit it to your teacher. For this project, you are expected to submit the following: 1. A proposal of the data collection design you plan to conduct, which includes the items requested below in step 3 or on the form provided by your teacher (and revised, if necessary, based on feedback from your teacher) 2. The collected data in a list or lists, if appropriate 3. The summary statistic(s) for the variable of interest Verification that the conditions are satisfied The complete inference procedure(s) 6. A written summary of your findings, including the answer to the question posed Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, email it to your teacher, or print it and hand in a hard copySuggested questions and topics: You may complete one of the following projects or select a question and inference procedure of your own with guidance from the teacher. Be sure to follow the procedures in this guide. Remember not to start gathering data until the teacher approves your proposal. Also, make any changes that your teacher suggests. Estimate the true mean time you wait for the bus in the morning to get to school. Randomly select 30 school days and record the amount of time you wait for the bus to arrive o Inference Construct a one-sample t interval for the mean time you wait for the bus to arrive Determine if a significant difference exists in the mean times to purchase a meal in lunch line A or in lunch line B. Randomly assign which days to use lunch line A and which days to use lunch line B. Record the times and which line was used each day. "Inference: Conduct a two-sided, two-sample t test for the difference in mean times. Determine if the mean time you can stand on your right foot is more than on your left foot. For each trial, randomly select which foot to use by flipping a coin. Time how long you can stand on that foot before you lose your balance. Record the time and the foot. After at least 20 trials are conducted on each foot, calculate the sample mean time for each foot Inference: Conduct a one-sided, two-sample r test for the difference in mean times Estimate the true proportion of students who use cell phones while in the school hallways. Select a random sample of students in the hallway. Count the number of students who are using cell phones and the total number of students selected. Calculate the sample proportion of students in hallways using cell phones. Inference: Construct a one-proportion z interval to estimate the true proportion of students using cell phones in the hallway. Determine if crinkled (or folded) entry papers for a drawing have a larger proportion selected than the proportion of crinkled papers that exist in the population. Place identical papers in a container with exactly 15% of those papers being crinkled. Mix the contents in the container well. Have people who do not know about the crinkled entries select 50 of the entry papers one at a time without replacement Count the number of selected papers that were crinkled. Inference: Conduct a one-sided, one-proportion z test to determine if the proportion of crinkled papers that would be selected from a container with 15% of the entries crinkled is more than 15% Determine if the proportion of games your favorite team wins when playing away games is less than when playing at home.Haye you eyer wondered why people acT The way they do on Black Friday or on the 4th ofJuly? Or why wealthy people and nations have less children than poorer ones? Or why we buy flowers. or a card for a loyed one knowing That itwill end up in The garbage later? Or why some countries are poor while others are rich? Or why some people liye longer in some parts of the world than others? Or why wars happen? These are among countless questions that could he answered through understanding the economics way ofthinking. This week, share an example from your life where you had to make a choice knowing that you are giying up opportunities for doing or gaining something else. Tell us about your thinking process and how you arriyed at the final choice you made. Would you make the same choice gain? Moreoyer, why do consumers make choices when They acquire something (jobs, money, friends, yacations, sleep, liying places, etc.}, and why do indiyidual producers or nations haye To choose The type, quality, and quantity of what they produce