What Is the Cauchy Distribution

One distribution of a random variable is important not for its applications, but for what it tells us about our definitions. The Cauchy distribution is one such example, sometimes referred to as a pathological example. The reason for this is that although this distribution is well defined and has a connection to a physical phenomenon, the distribution does not have a mean or a variance. Indeed, this random variable does not possess a moment generating function. Definition of the Cauchy Distribution We define the Cauchy distribution by considering a spinner, such as the type in a board game. The center of this spinner will be anchored on the y axis at the point (0, 1). After spinning the spinner, we will extend the line segment of the spinner until it crosses the x axis. This will be defined as our random variable X. We let w denote the smaller of the two angles that the spinner makes with the y axis. We assume that this spinner is equally likely to form any angle as another, and so W has a uniform distribution that ranges from -Ï€/2 to Ï€/2. Basic trigonometry provides us with a connection between our two random variables: X tanW. The cumulative distribution function of X is derived as follows: H(x) P(X x) P(tan W x) P(W arctanX) We then use the fact that W is uniform, and this gives us: H(x) 0.5 (arctan x)/Ï€ To obtain the probability density function we differentiate the cumulative density function. The result is h(x) 1/[Ï€ (1 x2) ] Features of the Cauchy Distribution What makes the Cauchy distribution interesting is that although we have defined it using the physical system of a random spinner, a random variable with a Cauchy distribution does not have a mean, variance or moment generating function. All of the moments about the origin that are used to define these parameters do not exist. We begin by considering the mean. The mean is defined as the expected value of our random variable and so E[X] ∠«-∞∞x /[Ï€ (1 x2) ] dx. We integrate by using substitution. If we set u 1 x2 then we see that du 2x dx. After making the substitution, the resulting improper integral does not converge. This means that the expected value does not exist, and that the mean is undefined. Similarly the variance and moment generating function are undefined. Naming of the Cauchy Distribution The Cauchy distribution is named for the French mathematician Augustin-Louis Cauchy (1789 – 1857). Despite this distribution being named for Cauchy, information regarding the distribution was first published by Poisson.

Access and Availability Two Challenges for Health Care

Access and Availability: Two Challenges for US Health Care Kaitnarine Harilal Walden University Access and Availability: Two Challenges for US Health Care The United States (US) health care system is changing dramatically. The Affordable Care Act is a catalyst that is spurring change by the promotion of two drivers: access and primary preventative care. Before the passage of the Affordable Care Act (ACA) in 2010, over 47 million Americans were uninsured thus denying them access to basic health care (U.S. Department of Health and Human Services [HHS], 2012). Increasing access and increasing the availability of primary care services (pre-natal care, preventative care, primary disease prevention, and secondary disease†¦show more content†¦The second major reform is to abolish TriCare, Medicare, Medicaid, and the Children Health Insurance Plan. This would establish one government system for all the elderly, poor, government workers, (to include military and veterans) and all children up to the age of 25. A single payer system would streamline billing by reduce administrative overhead necessary to manage clients from multiple payer systems. Shi amp; Singh (2012) agrees that this reform would provide benefits without penalty due to income level. However, such a system could become overburdened that may result in health care rationing (Shi amp; Singh, 2012). Access and availability of primary care providers are just two of many drivers that are shaping the health care industry. Passage of the ACA will result in improved access however the challenge of having enough primary care physicians for poor communities has not been properly addressed. Health care administrators in impoverished communities will have to be resourceful in attracting primary care providers to serve in their communities. The lesson provided by Cuba has shown that through their network of neighborhood clinics, preventative care can be successful (Bourne, Keck, amp; Reed, 2006). Cuba has shown that low cost care can result in health care outcomes that are comparable to the US (Bourne, Keck, amp; Reed, 2006). US health care is under going a transformation thatShow MoreRelatedThe Complex And Historical Problem Accessibility1306 Words   |  6 Pageshealthcare system. This is exceedingly difficult as each country is unique in their history, culture, population and health needs, all of which require a specialized system. Furthermore, an ideal system addresses equally the three key aspects of healthcare: quality, affordability and availability. A system without even one of these aspects at its full potential is not providing the best care possible for the population. Arguably, accessibility is the most crucial and challenging aspect. This is stillRead More1. Introduction . The Study Of Neighborhood Effects On1572 Words   |  7 Pages1. Introduction The study of neighborhood effects on health outcomes is a popular topic of interest among social scientists. Neighborhoods have the potential to affect an individual’s health as access to health care and proximity to medical facilities vary according to location. Previous studies demonstrate how affluent communities provide better public services for residents in comparison to low-income communities (Abramson 2015). Similarly, affluent communities tend to be safer, experiencingRead MoreConsidering The Spanish Country Perspective1626 Words   |  7 Pagesand dissemination towards the performance improvement of the health systems, the proposal involves the availability of the performance indicators in differentiated ways by the publishing of the report at three different levels: Government, Regional and Public. To embrace key stakeholders transversally across the EU countries, it was possible to identify three broad levels that will comprise different stakeholders depending on each health system configuration. The categorization of three primary levelsRead MoreHealth Disparities And Health System Barriers1745 Words   |  7 Pagesdefines Health Disparities as â€Å"the inequalities that occur in the provision of health care and access to health care across different racial, ethnic and socioeconomic groups.† This means Health disparities are essentially discrepancies in the servicing of Healthcare as well as in access to healthcare amongst people of different racial, cultural, and socioeconomic groups. Health Disparities has many underlying factors that impact it, a factor in particular is Health system barriers. Health system barriersRead MoreThe Millennium Development Goals ( Mdgs ) Essay1418 Words   |  6 Pagesmiscarriages occur mostly because of lack of proper medical care during the pregnancy period. In addition, about half a million women lose their lives every year during the period of pregnancy, delivery or post delivery (World Health R eport, 2005). Maternity care is thus very essential and governments need to ensure unlimited and unrestricted access by all women. Over the last thirty years, there has been an increased effort to improve maternal health accessibility and quality globally. Most of these initiativesRead MoreThe South East Asian Country Of Bangladesh1237 Words   |  5 Pages160,996,000 (Bangladesh). When Bangladesh is compared with India, it is evident that considerable progress is being made to improve the health of the people of Bangladesh. Nevertheless, there remain many areas of concern. Some of these concerns are the countries health development and provisions for healthcare delivery. There are differences in the overall health of the citizens of Bangladesh and those of India. In Bangladesh, the annual population growth rate and the adolescent fertility rate areRead MoreEthiopi A Country Living Of Poverty900 Words   |  4 PagesEthiopia are determined to rise above the challenges and put forth the effort to fix their state of poverty. In the following portfolio, the author will compare and contrast the key features in Ethiopia, observe the future challenges and directions that health care is striving to achieve, and describe the key contributions that help improve the health status in Ethiopia. Also, we will discuss the key organizations that will help Ethiopia overcome these future challenges. Key Features in Ethiopia and KenyaRead MoreTelemedicine : An Important Solution For Health Care Essay1556 Words   |  7 PagesFor many years, doctors and health service researchers have been searching about a new technologies in telecommunications to improve the health care. After a lot of work Telemedicine was implemented and become an important solution for health care consultations. The American Telemedicine Association (ATA) declared the Telemedicine as the use of medical information exchanged from one site to another via electronic communications to improve a patient s clinical health status[1]. So, in order toRead MoreMinimum Availability Of Health Personnel Essay988 Words   |  4 Pagesthat achieving Universal Health not only requires policy efforts to ensure an appropriate density of human resources for health (HRH), but also need to focus on ensuring an even geographic and social distribution of HRH, offering better economic incentives and work conditions to retain HRH in remote and underserved areas and prevent transnational migration, reshaping education programs to fit the new models of care based on a stronger first level of care and integrated health service delivery networksRead MoreElectronic Medical Records In Myanmar1747 Words   |  7 PagesIntroduction Background of the Study Poor health information system has been a major challenge in healthcare delivery in many developing countries due to limited financial resources. Health information technology provides to collect, organize and present medical information in a system that will make it useful to all healthcare professionals (Robert E Hoyt, 2014). Electronic medical records (EMR) are a vital and basic part of the implementation of information technology in the healthcare industry

Assessment Task Carbon Chemistry and Functional Groups Free Essays

Assessment Task:Â  Carbon Chemistry Functional Groups 1. Why does the carbon atom make so many covalent compounds? Carbon atoms have 4 single valence electrons, which mean they can bond to 4 other atoms. It bonds in a tetrahedral shape, or make straight, bent or ring shaped molecules when many are bonded together. We will write a custom essay sample on Assessment Task: Carbon Chemistry and Functional Groups or any similar topic only for you Order Now The complexity allows it to bond to many other atoms. (1) 2. How is the structure of ethanol (key ingredient in vodka) different than the structure of acetic acid (vinegar) in terms of functional groups? Firstly, the structure of ethanol contains 6 hydrogen atoms, 2 carbon atoms and an oxygen atom. What is different from ethanol is that acetic acid has 2 oxygen atoms bonded to it rather than one and there are 5 hydrogen atoms on acetic acid while there are 6 hydrogen atoms on the ethanol. On the ethanol, the oxygen and a hydrogen atom bond together to form a hydroxyl group at the end of the chain while there is a carboxyl group attatched to the main chain of the acetic acid. The aldahyde functional group contains a double bond oxygen atom and a hydroxy group bonded to the end carbon. (1) 3. Draw diagrams of ethanol and acetic acid – clearly showing the shared pairs of electrons (covalent bonds). 4. Draw a structural diagram of glycine. (2) 5. Name the class of compounds that glycine belongs to and what do all of the compounds in this class have in common? Glycine is in the class of macromolecules. Ths class includes many repeated functional groups. 1) 6. Draw an organic compound that has two different functional groups. Lable these groups. Hydroxyl group on one end carboxyl group on the other. References 1. Allinotte, T. (2008). Chemical Basis of Life. Retrieved from www. virtualhighschool. com/d2l/orgTools/ouHome/ouHome. asp? ou=58018amp ;gt; on December 28, 2011. 2. Wales, J. (2011). Glycine. Retrieved from http://en. wikipedia. org/wiki/Glycine on December 28, 2011. How to cite Assessment Task: Carbon Chemistry and Functional Groups, Papers

Feeling Glamorous Essay Example For Students

Feeling Glamorous Essay I was less nervous on this particular Saturday than I anticipated. This is after all, the day that every woman dreams of, her wedding day! My head was intensely pounding from the previous nights celebration. If I could give advice to any engaged couples- have your â€Å"last night out† parties weeks before the wedding! Luckily for me, my maid of honor anticipated how I’d feel, she put Tylenol and bottled water on my night stand. I took my time making my way downstairs, even though I could hear all of my family in the kitchen. I had told them all several days in advance â€Å"It’s an evening wedding, sleep in and relax. No one should be stressed out. † I tried to walk into the kitchen as nonchalant as possible, however as soon as my mother saw me she burst into tears! â€Å"Stop that! You’ll be a red, puffy eyed and red nosed in all the pictures. You better all get it out now before we go for hair and make-up at the salon. † I said. You see, I was the last of 6 daughters to get married. My father passed several years ago and my grandfather passed the year prior, I was the last and only one walked down the aisle with my mother. Once brunch was eaten and everyone had calmed their nerves, I suggested to relax in the sun. It’s not often that my family can all get together besides major holidays- this was such a blessing. We all lounged on the back deck where time seemed to pass in slow motion. Perhaps we were quietly bracing ourselves for the frenzy that would follow as the day progressed. All the women of the family, as well as my female soon-to-be in-laws headed off to the salon. Luckily for me this salon had a private room so I was able to have peace while everyone else sounded like school girls. Thinking back, I believe some of them were more excited about my wedding than I was. Before anyone realized, time had started speeding by. We had been at the salon for five hours and my wedding was due to start in less than two! I decided to leave the salon with my maid of honor while the rest of the girls finished hair and make-up. As I walked downstairs and entered the room I had turned into what appeared to be a wedding boutique, it hit me! It was as if someone had punched me in the gut and knocked the wind out of me. I started sweating and had the horrible watery mouth sick taste right before you vomit- it was horrible! I scanned the room, doing a mental checklist, and caught a glimpse of my reflection in the mirror. I froze, the woman in the mirror was someone I didn’t recognize. I am a simple girl- minimal make-up, ponytail, jeans and t-shirt kind of girl. The woman in the mirror was someone I didn’t recognize. With my hair pinned up in curls, glossy red lips and just enough eye shadow to enhance the blue in my eyes I was ready to put my dress on. I wanted to be fully dressed, ready to walk down the aisle an hour before the ceremony was to start. Fortunately, my wedding crew returned in enough time therefore my mom could help me get dressed. I had my dress at my mothers for months, so no one could see it until today. I truly had forgotten how beautiful it was! I wore a white, A-line, hand embroidered wedding dress with a train and crystals sewn all over resembling fireworks. Looking in the full mirror, I had the same feeling as earlier, like the wind was sucked out of my body. .u366ab8009e015805d162218d9422488b , .u366ab8009e015805d162218d9422488b .postImageUrl , .u366ab8009e015805d162218d9422488b .centered-text-area { min-height: 80px; position: relative; } .u366ab8009e015805d162218d9422488b , .u366ab8009e015805d162218d9422488b:hover , .u366ab8009e015805d162218d9422488b:visited , .u366ab8009e015805d162218d9422488b:active { border:0!important; } .u366ab8009e015805d162218d9422488b .clearfix:after { content: ""; display: table; clear: both; } .u366ab8009e015805d162218d9422488b { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u366ab8009e015805d162218d9422488b:active , .u366ab8009e015805d162218d9422488b:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u366ab8009e015805d162218d9422488b .centered-text-area { width: 100%; position: relative ; } .u366ab8009e015805d162218d9422488b .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u366ab8009e015805d162218d9422488b .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u366ab8009e015805d162218d9422488b .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u366ab8009e015805d162218d9422488b:hover .ctaButton { background-color: #34495E!important; } .u366ab8009e015805d162218d9422488b .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u366ab8009e015805d162218d9422488b .u366ab8009e015805d162218d9422488b-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u366ab8009e015805d162218d9422488b:after { content: ""; display: block; clear: both; } READ: Friendship theme from lord of EssayI couldn’t help but stare at my own reflection for what seemed like several minutes. At that moment I knew I would never feel better about myself. Never in my life have I felt as glamorous as I looked in the mirror that day. Not to sound like a cynic, I do not believe I will experience anything like it again in my lifetime. My wedding rings are now off, vows in front of family, friends and God have sadly been broken. Even through all the pain that followed this wonderful day, remembering seeing my reflection can still bring a smile to my face.