How to Calculate the Median of Exponential Distribution

How to Calculate the Median of Exponential Distribution The median of a set of data is the midway point wherein exactly half of the data values are less than or equal to the median. In a similar way, we can think about the median of a continuous probability distribution, but rather than finding the middle value in a set of data, we find the middle of the distribution in a different way. The total area under a probability density function is 1, representing 100%, and as a result,  half of this can be represented by one-half or 50 percent. One of the big ideas of mathematical statistics is that probability is represented by the area under the curve of the density function, which is calculated by an integral, and thus the median of a continuous distribution is the point on the real number line where exactly half of the area lies to the left. This can be more succinctly stated by the following improper integral. The median of the continuous random variable X with density function f( x) is the value M such that: ï » ¿0.5∠«m−∞f(x)dx0.5\int_{m}^{-\infty}f(x)dx0.5∠«m−∞​f(x)dxï » ¿ Median for Exponential Distribution We now calculate the median for the exponential distribution Exp(A). A random variable with this distribution has density function f(x) e-x/A/A for x any nonnegative real number. The function also contains the mathematical constant e, approximately equal to 2.71828. Since the probability density function is zero for any negative value of x, all that we must do is integrate the following and solve for M: 0.5 ∠«0M f(x) dx Since the integral ∠« e-x/A/A dx -e-x/A, the result is that 0.5 -e-M/A 1 This means that 0.5 e-M/A and after taking the natural logarithm of both sides of the equation, we have: ln(1/2) -M/A Since 1/2 2-1, by properties of logarithms we write: - ln2 -M/A Multiplying both sides by A gives us the result that the median M A ln2. Median-Mean Inequality in Statistics   One consequence of this result should be mentioned: the mean of the exponential distribution Exp(A) is A, and since ln2 is less than 1, it follows that the product Aln2 is less than A. This means that the median of the exponential distribution is less than the mean. This makes sense if we think about the graph of the probability density function. Due to the long tail, this distribution is skewed to the right. Many times when a distribution is skewed to the right, the mean is to the right of the median. What this means in terms of statistical analysis is that we can oftentimes predict that the mean and median do not directly correlate given the probability that data is skewed to the right, which can be expressed as the median-mean inequality proof known as Chebyshevs inequality. As an example, consider a data set that posits that a person receives a total of 30 visitors in 10 hours, where the mean wait time for a visitor is 20 minutes, while the set of data may present that the median wait time would be somewhere between 20 and 30 minutes if over half of those visitors came in the first five hours.

Intercontinental Hotels Group

Intercontinental Hotels Group Introduction Many countries in the world depend on the travel and hospitality industry as the major source of revenue. Indeed, the travel and hospitality industry plays a significant role in economic emancipation. In today’s technologically advancing world, and competitive business markets, various organizations must come up with new strategies in order to retain customers and even attract others. Additionally, many business segments focus on modalities of expanding their portfolios in order to increase their market share.Advertising We will write a custom report sample on Intercontinental Hotels Group Green Engage sustainability system specifically for you for only $16.05 $11/page Learn More In this new area of technological revolution, organizations engage in other activities in order to please their customers. In fact, the main role of corporate events in any organisation or company is to entertain clients so that they become happier than they wer e before. This is the reason why many organizations continue to employ new strategies in order to attract prospective clients (Holcomb, Upchurch Okumus, 2007, pp. 461-475). The Intercontinental Hotels Group’s corporate hospitality section is expanding at a fast rate and many clients consider it one of the best. This is simply because the sector has mastered the art of linking spectators and activities in order to offer judicious hospitality products and services to clients. Owing to these facts, the intercontinental hotels group has the responsibility of retaining and attracting new customers by adopting new strategies. This report will assess the intercontinental hotel group – green engage sustainability system as a corporate hospitality event (Paton, 2007, pp. 46-49). Intercontinental Hotels Group Intercontinental Hotels Group undoubtedly runs the biggest multinational hotels in the world. The group has its headquarters in Denham, United Kingdom. It has over 4000 ho tels across the globe and enormous accommodation spaces. It also has several brands such as Holiday Inn Express, Hotel Indigo and Even. Other brands include Intercontinental and Candlewood Suites. One of the most common features about these hotels is that they run under franchise agreements. In other words, the company runs the affairs of the hotels, but different stakeholders own them. Of all the hotels under the group, investors only own and manage ten. The International Hotels Group also has listed some of its shares in major trading stock markets. For instance, FTSE 100 index, London Stock Exchange, and New York Stock Exchange are some of the stock markets that have listed International Hotels Group shares. Primarily, the Intercontinental Hotels Group manages all hotels owned by the group.Advertising Looking for report on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More It also performs other functions such a s franchising the IHG brands in order to attract customers. The hotel mainly involves itself in hospitality activities such as hotel management, accommodation, creation of systems, and sales and marketing of their products. The owners are responsible for the construction of new hotels and coming up of new structures to house other services. This is simply because these activities need risk profiling; require enormous management skills and capital to run. So far, the group has sixteen corporately owned hotels that use the brand (Intercontinental Hotel Group, 2013, p. 1). Green Engage sustainability system The intercontinental hotel group owns the best hotel brands in the world, but it also understands that the change of climatic conditions affects their business. Like any other organisation, IHG commits itself towards reducing energy, carbon, and other substances that destroy the environment. The group is also committed towards clean energy, as a way of minimizing emissions. For inst ance, in the past, the management has resorted to other means of energy by stopping the purchase of carbon commodities. The group has also collaborated with other developers to identify and implement not only cost-effective, but also sustainable technology. We have seen that IHG has over 4500 hotels. Furthermore, the stakeholders are doing all they can in order to introduce clean technology into their business portfolios. The stakeholders have also put in place mechanisms to ensure that the hotel not only complies with climate change patters, but also adopts sustainable technologies. We now that green technology is evolving at a fast rate. In order to meet the demands of green technology, the group has employed professionals to explore new designs that are sustainable (Intercontinental Hotel Group, 2013, p. 1). Green Engage System Some few years ago, the Intercontinental Hotels Group unveiled its online sustainability system to check compliance of sustainability. This system plays a significant role in ensuring that all IHG hotels not only conserve resources, but also save money. In order to realize this, the system proposes constant measuring and reporting of waste consumption, water consumption and hotel energy. This is important because it will reduce the skyrocketing energy costs.Advertising We will write a custom report sample on Intercontinental Hotels Group Green Engage sustainability system specifically for you for only $16.05 $11/page Learn More In fact, energy costs have been major concerns to owners who have witnessed the rising energy prices lower their profits and threaten their businesses. The taxation of carbon fuels also threatens the operations of the hotels and therefore, there was need to look for new and sustainable ways of energy. There is no doubt that by unveiling this system, the intercontinental hotels group showed its commitment towards ensuring sustainability. Since the unveiling of the system, stakeholders have received the system without complains. There has been consensus among stakeholders and all of them believe that the system is good to their business. In fact, this has led to the certification of the system making IHG the first hotel in the world to receive such accreditation. Many stakeholders believe that the system is advantageous especially to environmental sustainability, and provides mechanisms of ensuring sustainability. Moreover, the reason why stakeholders approved the system is that it routinely creates reports and sets new energy benchmarks in order to make comparisons with other useful data. The system also plays other significant roles such as providing green solutions, and generating new and sustainable hotel designs. The system also provides information on new ways of reducing the impacts brought about by non-sustainable energy sources. Notably, the green engage system functions like a library of information to stakeholders. For instance, the green engage system has information on selecting suitable site for development, and choosing the right lighting for a particular hotel. This happens through selecting conscientious cleaning materials and training of employees on issues of sustainability. Since the adoption of the system, stakeholders continue to realize their return of investment. Additionally, the system has led to the reduction of carbon emissions and increased the number of guests thus, generating more revenue (U.S. Department of Energy, 2013, p. 1). Benefits of the Green Engage System to stakeholders The biggest beneficiaries of the green engage system are the stakeholders. To start with, the system has enabled the IHG hotels to save over 25 percent of energy. This translated to over $300 million, money that the group can invest elsewhere. So far, over 3000 hotels under the group have adopted the system and the management expects all hotels to adopt the system soon. Stakeholders believe that the green engage system offers consider able competitive edge towards ensuring sustainability. For instance, through the system, the IHG hotels have become cost-effective. This means that it is able to offer better and improved services that will only attract more prospective customers, but also retain them. There is no doubt that many clients prefer to stay in ‘green’ rooms, and this desire enabled IHG to win a contract worth  £300,000 annually for seven consecutive years (Mayock, 2011, p. 1).Advertising Looking for report on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Culture Shift By adopting the green engage system, the intercontinental hotel group has adopted a new culture of ensuring sustainability. Unlike the past, the green engage system provides information on the levels of sustainability, tracks the process of sustainability, and releases progress reports that indicate areas to improve. Notably, in a highly competitive travel and hospitality market, the adoption of the system marked a culture shift that not only recommends green technology solutions, but also encourages competition. There is no doubt that the system has introduced a culture shift in the hospitality industry for sustainability reasons. For instance, the green engage system provides a calculator that hotel managers can use to calculate the carbon footprint. Consequently, if it is high, then they can look for ways of minimizing it (EcoCommericial Building, 2013, p. 1). Conclusion The green engage system developed by the intercontinental hotels group is a step towards ensurin g clean energy. Since its adoption, the company has managed to reduce carbon footprints thus reducing the rising energy costs. Most importantly, many visitors enjoy staying in the IHG ‘green’ hotels. References EcoCommericial Building, 2013, The effort to be sustainable from the hotel groups,   http://china.ecocommercial-building-network.com/2013/02/21/the-effort-to-be-sustainable-from-the-hotel-groups/. Holcomb, J. L., Upchurch, R. S., Okumus, F., 2007, ‘Corporate social responsibility: What are top hotel companies reporting’, International Journal of Contemporary Hospitality Management, vol. 9 no. 6, pp. 461-475. Intercontinental Hotel Group, 2013, Corporate Responsibility Report: Green Engage,   ihgplc.com/index.asp?pageid=742. Mayock, P 2011, IHG reaps energy savings with Green Engage, hotelnewsnow.com/articles.aspx/5089/IHG-reaps-energy-savings-with-Green-Engage. Paton, N 2007, ‘Giving something back’, Caterer Hotelkeeper, vol. 197 no. 4496, pp. 46-49. U.S. Department of Energy, 2013, Showcase project: Intercontinental Hotel Group,   http://www4.eere.energy.gov/challenge/partners/better-buildings/intercontinental-hotels-group.

Supervise vs. Monitor

Supervise vs. Monitor Supervise vs. Monitor Supervise vs. Monitor By Maeve Maddox A reader wants to know if there’s a difference between the verbs supervise and monitor. Both are synonyms for the act of overseeing the execution of a task or activity. Some speakers use them interchangeably, but they do differ in connotation. Supervise implies more interaction than monitor. Supervisors have the responsibility of informing and directing, while monitors observe without instructing. A person who supervises children is expected to step in if they behave contrary to expectations; a person or machine engaged in monitoring an activity is not generally expected to deal directly with a problem, but to alert a person in charge. The noun form for supervise is supervisor; monitor serves as noun as well as verb. A supervisor is always human; a monitor may be a human being or a machine. Monitor comes from Latin monere, â€Å"to warn.† It’s the monitor’s job to warn someone that some activity is not proceeding according to plan. You might monitor your utility bills by keeping track of the monthly increases and decreases. The Yankees also will monitor what the Brewers do with Rickie Weeks, who could be beaten out at second base by Scooter Gennett. Just asking a child to monitor their own behavior will increase the behavior that you want and reduce the behavior you do not want to see. Sometimes a monitor may be expected to act, but only in an extreme situation requiring immediate attention. Police expected to monitor Rizzuto funeral visitation closely Another noun for the person who oversees the work of others is overseer, a word which can bear a negative connotation. Historically, an overseer was in charge of slaves or, in Australia, a band of convicts. In modern Australian usage, an overseer is the manager of a sheep station or other rural property. In American usage, an Overseer is a member of a university governing board, or a religious leader. In general American usage, however, overseer is still strongly associated with slavery; think Jonas Wilkerson in Gone With the Wind. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Misused Words category, check our popular posts, or choose a related post below:7 English Grammar Rules You Should KnowSelect vs. SelectedList of 50 Compliments and Nice Things to Say!

John Steinbeck Research Paper Example | Topics and Well Written Essays - 1250 words

John Steinbeck - Research Paper Example The lower part of the Salinas valley was a shipping center. The demographic and the geographic location characteristics of John Steinbeck’s hometown were great factors that influenced a majority of his novels and indicated his characters had a strong identification with the land. Steinbeck even wrote to George Albee in 1933 telling him that he wanted to write the story of the entire valley, all the small towns and farms and all the ranches located in the wilder hills. Steinbeck had a comfortable childhood period in Salinas, though as a teenager his family faced numerous setbacks. His adorable father who had been working as a manager in Sperry Flour lost his job. He worked out his second option of opening a grain and feeds store, but unfortunately it failed too. Eventually, he was in a position to secure a job in Monterey County as the treasurer. Steinbeck loved his pony, which he named Jill, and this inspired him to write his later novel entitled â€Å"The Red Pony†. His writing career was greatly affected by his childhood even ts. On his ninth birthday, someone gave him a copy of Thomas Malory’s work, and he admits that when he first read it, he was charmed of words because the old fashioned words delighted him (Steinbeck 97). He keenly read the stories of King Arthur, and together with his sister, they would visualize the towers of Camelot amidst the sandstone erosions alongside the Pastures of Heaven where his aunt resided. Twenty years down the line, he adopted Arthurian tropes besides chapter headings of his novel Tortilla Flat. Steinbeck in his career would travel to England to prepare how the Arthurian tales would be updated for modernity. His mission wasn’t complete until his demise but his Noble Knights and Acts of King Arthur were later published posthumously. As a teenager, John Steinbeck displayed a robust interest in writing and in his high school days, he would work until the

Gay, Lesbians, and Mental Illness Research Paper

Gay, Lesbians, and Mental Illness - Research Paper Example This is so because mental health personnel and society at large were given biased information, to begin with. The resultant conclusions were biased too because some time ago, only those gay/lesbians undergoing medical treatment were involved in the studies. But it soon became apparent that homosexuality was not a mental syndrome when researchers studied data of those who were not undergoing therapy. It was not only the mental health professional themselves who were guilty of this belief. Until 1973, even a prestigious organization as the American Psychiatric Association was guilty of this practice for they used to include homosexuality in the official manual that listed mental and emotional disorders. And it took American Psychological Association another two years to pass the resolution supporting the action of the APA. Some people still cling to the idea that mental illness is associated with homosexual orientation. It was the new and better-designed research methods that helped turn the tables in reaching this momentous decision on behalf of the gay/lesbians. Now, all concerned are in agreement that homosexuality is not an illness, mental disorder or an emotional problem. But it was not until more than three decades have passed that the situation was finally remedied. It is gratifying to note that much research has been done on the subject. Tori DeAngelis is a writer who is based in New York. She writes prolifically on homosexuality and related issues. She unearths valuable data on the lesbian/gay and bisexual (LGB) mental health and states that new findings overturn beliefs that were held previously inviolable. She reports on some of the new ‘breakthrough studies’ that offer fresh insights into the mental state of gay/lesbians. According to her, many such studies indicate that compared to heterosexuals, gay/lesbians seem to have higher rates of mental disorders.  Of course, this does not rise to the levels of serious pathology.  Ã‚  

CITI business case study Example | Topics and Well Written Essays - 1750 words

CITI business - Case Study Example Increased competition for capital continues to force banks to innovate (Citibank, 2008). In order to differentiate its e-business products from those of its competitors, Citibank took several measures(Citibank, 2008). First, the bank developed a strategy for its corporate banking division where its target corporate clients included multinational corporations (MNCs), financial institutions, government agencies, local enterprises and SMEs. The bank understood that each of these corporate client categories had unique needs. The bank realized to need to go the extra mile to package its products to meet the unique needs of every customer (Citibank, 2008). Citibank also differentiated itself and its products from those of its competitors through an improved, comprehensive customer service. The customer service includes telephone hotlines, relationship managers who take their time to comprehend the individual customer’s needs and product advisors whose role is to advise customers on the product or products that most suits its needs. Finally, the bank continues to invest heavily in technology in order to promote both the front- and back-end electronic banking systems. Besides, the bank seeks to make itself more accessible to its customers through what is calls its unified platform. The platform uses a teamwork approach that allows the bank to work with every function in the organization of the client (Citibank, 2008). Grow its global reach: As at the time of developing this strategy in 2008, Citibank had operations in 100 countries of the world and employed over 268,000 people. This global presence, the bank believes, puts it in a strong position to meet the global needs of its customers. This being the case, the bank should continue its global expansion drive. Strengthen its brand: The bank believes that it has built a strong brand

Persuasive Message Essay Example | Topics and Well Written Essays - 500 words - 2

Persuasive Message - Essay Example As such, we have come up with detailed and more complex ways of handling cleaningness as one of the more imperative outsourcing projects. Apparently, we are aware that numerous companies have claimed to offer cleaning services in the market but have ended up doing the exact opposite. However, at Marcus-Fortune Cleaning Agency we believe that ‘COMFY DEMANDS CLEANINGNESS’. In this regard, we are equipped to offer probation services at affordable fees to act as an expression of our undoubted services upon your approval and cooperation. Marcus-Fortune Cleaning Agency as a cleaning agency offers services such as essential cleaning for offices, hospitals, schools, churches, hotels among other institutions. In addition, it offers moving services for offices and residential places for both private and public properties. Another service that we offer comprises of providing hygiene bins, collecting, and replacing them for use in washroom and recreational facilities in their respected institutions and organizations. It is for this undoubted reason that Marcus- Fortune Cleaning Agency is at your service to ensure that the level of cleaningness has met you comfort. At Marcus- Fortune Cleaning Agency, you are assured of getting the highest level of cleaningness that gives you the utmost comfort required. In addition, we have a dedicated working rot that is willing to retain its professionalism while working towards satisfaction of its potential customers. We have incorporated a comprehensive brochure of the agency, for your perusal. We anticipate for convenient meetings where we could discuss the likelihood of working with you in future. As such, we will contact you sooner than later for the possibility of setting up meetings at your convenience. You can also visit our website at www.marcusfortuneagency.uk for more information on the