Chebyshevs Inequality in Probability

Chebyshev’s inequality says that at least 1-1/K2 of data from a sample must fall within K standard deviations from the mean (here K is any positive real number greater than one). Any data set that is normally distributed, or in the shape of a bell curve, has several features. One of them deals with the spread of the data relative to the number of standard deviations from the mean. In a normal distribution, we know that 68% of the data is one standard deviation from the mean, 95% is two standard deviations from the mean, and approximately 99% is within three standard deviations from the mean. But if the data set is not distributed in the shape of a bell curve, then a different amount could be within one standard deviation. Chebyshev’s inequality provides a way to know what fraction of data falls within K standard deviations from the mean for any data set. Facts About the Inequality We can also state the inequality above by replacing the phrase â€Å"data from a sample† with probability distribution. This is because Chebyshev’s inequality is a result from probability, which can then be applied to statistics. It is important to note that this inequality is a result that has been proven mathematically. It is not like the empirical relationship between the mean and mode, or the rule of thumb that connects the range and standard deviation. Illustration of the Inequality To illustrate the inequality, we will look at it for a few values of K: For K 2 we have 1 – 1/K2 1 - 1/4 3/4 75%. So Chebyshev’s inequality says that at least 75% of the data values of any distribution must be within two standard deviations of the mean.For K 3 we have 1 – 1/K2 1 - 1/9 8/9 89%. So Chebyshev’s inequality says that at least 89% of the data values of any distribution must be within three standard deviations of the mean.For K 4 we have 1 – 1/K2 1 - 1/16 15/16 93.75%. So Chebyshev’s inequality says that at least 93.75% of the data values of any distribution must be within two standard deviations of the mean. Example Suppose we have sampled the weights of dogs in the local animal shelter and found that our sample has a mean of 20 pounds with a standard deviation of 3 pounds. With the use of Chebyshev’s inequality, we know that at least 75% of the dogs that we sampled have weights that are two standard deviations from the mean. Two times the standard deviation gives us 2 x 3 6. Subtract and add this from the mean of 20. This tells us that 75% of the dogs have weight from 14 pounds to 26 pounds. Use of the Inequality If we know more about the distribution that we’re working with, then we can usually guarantee that more data is a certain number of standard deviations away from the mean. For example, if we know that we have a normal distribution, then 95% of the data is two standard deviations from the mean. Chebyshev’s inequality says that in this situation we know that at least 75% of the data is two standard deviations from the mean. As we can see in this case, it could be much more than this 75%. The value of the inequality is that it gives us a â€Å"worse case† scenario in which the only things we know about our sample data (or probability distribution) is the mean and standard deviation. When we know nothing else about our data, Chebyshev’s inequality provides some additional insight into how spread out the data set is. History of the Inequality The inequality is named after the Russian mathematician Pafnuty Chebyshev, who first stated the inequality without proof in 1874. Ten years later the inequality was proved by Markov in his Ph.D. dissertation. Due to variances in how to represent the Russian alphabet in English, it is Chebyshev also spelled as Tchebysheff.

GB511C Strategic Resources Management Final Exam Essay

GB511C Strategic Resources Management: Final Exam Adam J. Franco Norwich University Professor Laurette Brady November 16, 2013 Manufacturing today includes all facets of research, development, production, sales, distribution, logistics, customer service, marketing, and support. It extends from the making of physical products to the delivery of services (Deloitte, 2013). Manufacturing companies now compete on a global scale and utilize specific locations around the world to their advantage. For instance, basic, simple to make products will be produced in an area with cheap, low education labor. While products that use high tech machinery that require a skilled labor force would need to be produced†¦show more content†¦For this manufacturing company they would have to produce their high-end items in the United States and would probably benefit from establishing their headquarters in the US as well. The security and elaborate IT infrastructure of the United States will increase their ability to command and control their global operations in Mexico, Turkey, and France. Mexico Mexico is the United States’ second-largest export market and third-largest trading partner. Many large global companies have chosen to locate significant manufacturing operations in Mexico, particularly along the U.S. Mexican border (TACNA, 2013). Mexico is in a strategic location to large US consumer base. Many US companies manufacture their goods in Mexico and use trade agreements and established distribution channels to flood the American market. The human capital in Mexico has significant advantages to a manufacturing company. Their labor cost are about 25% lower then the United States, and the laborers work a standard 48 hours work week (TACNA, 2013). In the last couple of decades, Mexico has dramatically increased its numbers of university and technical schools. This investment in education instills confidence that a technically capable workforce will only grow in size in the future. Organizational capital in Mexico is not as significant a hurdle as in other locations. One of the biggest miscalculations that Western business people make when dealing with Asian cultures is the huge culture gap. â€Å"In

Belonging to Culture Free Essays

People feel a strong sense of belonging to their culture. This is seen in the film ‘Bend It Like Beckham’ by Gurinder Chadha. The main scenes that portray this statement are the engagement scene, pre-wedding scene and the wedding scene. We will write a custom essay sample on Belonging to Culture or any similar topic only for you Order Now This statement is also shown in the related text ‘Integrated’ by Sylvia Kantaris. In the film, various techniques are used such as long shots, full shots and panning. In the related text the techniques used are a metaphor, listing, contrast and emotive words. In the film ‘Bend It Like Beckham’ the engagement scene starts off with a long shot of the outside of Jessminder’s house. The house is decorated with lights and lighting is a technique used to make the house stand out. After that there is a high angle/close up shot of the food. The foods are colourful and bright. Bright colours are festive and symbolises happy occasions. Costume is another technique. Everyone is wearing the same sort of clothing and they are colourful. This shows that they belong to the Indian culture. The full/long shot of the room and the people sitting next to each other shows sense of belonging to their culture. This scene also explores gender roles. The males were sitting down, eating and talking to others whilst Jess was walking around offering food to the guests. A woman tells Jess â€Å"it will be your turn soon. † This means that she is expected to marry an Indian man just like every other Indian woman. These values and traditions are aspects of their Sikh Indian culture and Jess is expected to follow them. People feel a strong sense of belonging to their culture. We also see this in the pre-wedding preparation scene. In this scene we see everyone sitting together again. Gender roles are explored in this scene as well. All the women are sitting next to each other around a table making samosas. A full shot is a technique used in this scene. This shows belonging to their culture because they are all celebrating harmoniously. There are alternations used between the Indian and British culture to show contrast between the two cultures. There is an overhead shot of the Bhamra’s backyard and their neighbours backyard. The Bhamra’s backyard is colourful, active and bright while their neighbours backyard is quiet, dull and empty. There are alternations used between Jess preparing for the wedding and her team training for the finals. This shows that she is caught between two cultures. Music is a technique used. The music is sad and so is Jess. Her facial expressions show us that she is not interested in what’s going on around her. She takes down her David Beckham poster and this shows that she is giving up on soccer. People feel a strong belonging to their culture however some people can feel caught between two cultures. Another text that that shows people feel a strong sense of belonging to their culture is the poem ‘Integrated’ by Sylvia Kantaris. This poem is about a Greek woman who moves into Australia but does not want to integrate. The metaphor â€Å"she brought her country with her in packing cases† tells us that she has brought ornaments of her country with her because she feels strongly about her culture. She does not want to integrate because she is scared of losing her own culture. At her home in Australia, she listens to Greek music, speaks Greek with her granddaughter and this shows she feels strongly about her culture. Another technique used in this poem is listing. First there is a listing of all the Greek items and then there is a listing of Australian items. This shows contrast between two cultures. Her granddaughter listens to western music, speaks English and eats Australian food. â€Å"Her grandchild†¦has eaten corned-beef, cornflakes†¦another tongue, her future. † This quote tells us her granddaughter has found it quite easy to integrate whereas â€Å"the land gave way, she arranged it to her liking,† shows the grandmother got her way. The use of emotive words such as â€Å"fierce† and â€Å"confrontation† shows that there was a battle between the grandmother and her new environment and she won because she did not integrate. Australia is more malleable than she,† tell us Australia was manipulated because the grandmother did not give up. She kept to her culture. Not only do people feel a strong sense of belonging to their culture but they can experience cultural clash. In conclusion people feel a strong sense of belonging to their culture. This is seen in the film ‘Bend It Like Beckham ’ and the poem ‘Integrated. ’ Both of these texts show us people feel strongly about their culture. However they also show us that cultural clashes can arise as well when people feel trapped between two cultures. How to cite Belonging to Culture, Essay examples

Nassar v Innovative Precasters Group Pty Ltd †MyAssignmenthelp.com

Question: Discuss about the Nassar v Innovative Precasters Group Pty Ltd . Answer: Introduction The Corporations Act, 2001 (Cth) is the main legislation which is applicable for the companies in Australia. Through Part 2D.1 of this act, the directors and the officers of the companies have been given certain duties, which have to be fulfilled as a statutory requirement (Latimer, 2012). Apart from this, the commonlaw also imposes certain duties on the directors, which have to be adhered to in a strict manner. The reason for this is that a breach of director duties results in pecuniary penalties, disqualification orders and even attracts criminal liabilities (Cassidy, 2006). Nassar v Innovative Precasters Group Pty Ltd (2009) NSWSC 342 was one of the cases where the court concurred that there was the need for mutual cooperation and a particular trust level for running the day to day management of the company in a smooth manner. The court in this stated that the winding up of the company, based on the present circumstances, was merely a remedy to the situation which was present, where the working relationship required trust, confidence and mutual co-operation and these were broken down (Chamberlains, 2017). The following parts analyses this case, particularly in terms of the duties and responsibilities which were contravened. Nassar v Innovative Precasters Group Pty Ltd (2009) In this case, the proceedings were related to the activities carried on by the individuals regarding the three companies that had been created and owned by them, i.e., the Innovative Precasters Group Pty Ltd, herein referred to as IPG, the IP Group Pty Ltd, herein referred to as Group, and the DGN Investments Pty Ltd, herein referred to as DGN, and these three were the defendants of this case, along with the others. In the first company, the shares were held by Marfern Pty Ltd and by the two companies respectively held by Grass and Oliveira. In the latter two companies, Nassar, Grasso and Oliveira were the only directors (Australasian Legal Information Institute, 2009a). The allegations which were made in this case were related to thlawe affairs of the company not been conducted in a proper manner as they were contrary to the members interests as a whole, owing to the conduct being unfairly prejudicial or oppressive or unfairly discriminatory particularly against the plaintiffs of this case (McInerney, 2015). Nassar and Marfern made the claim against the two companies in which they were shareholders and Nassar alone made a claim for the company in which Marfern was not a member. The key relief which the plaintiff sought was the three companies to purchase the shares of the plaintiff and the alternative claim was for the company to be wound up (Jade, 2009). Duties/ Responsibilities breached The directors of each and every company owe certain duties towards the shareholders of the companies. This is in particular reference to protection of the minority shareholders, owing to the far reaching remedies which are given to the oppressed minority shareholders (Paolini, 2014). The directors have the duty under section 181 whereby the directors and the key officers of the company have to use their powers and fulfil their obligations for the proper purpose, in good faith and in the best interest of the company (Australasian Legal Information Institute, 2017). The breach of this section attracts civil penalties under section 1317E of this act (Federal Register of Legislation, 2017). Derived from this duty is the duty of the directors towards the interests of all the shareholders. The duty towards minority shareholders of the company is enhanced because the minority shareholders do not have the ability of influencing the affairs of the company. Hence, it is important for the directors to act fairly for these shareholders and make it their duty to ensure that the decisions taken by them promote the interest of all the shareholders and the company. In case the directors fail to do so, they not only breach their statutory duties, but also have the risk of being engaged in oppressive conduct, where section 232 and 233 apply (Easton, 2013). The basis of the claim was the oppressive conduct of the management of the company and so, the section 232 and 233 were applied. The statutory jurisdiction which is created under these sections provides a way through which the legal rights can be looked beyond by the court and such action is undertaken which is equitable and just. The partnership between Oliveira and Grasso was a key part which led to the oppression in this case. Though, this claim of the plaintiff could not stand. In order to hold Oliveira and Grasso liable, it was shown before the court that they had failed in taking the requisite steps, which was required on by being the directors of the company. They failed to avoid the conduct which was unfairly discriminatory, unfairly prejudicial or oppressive conduct, which was a mechanistic and simple approach (Jade, 2009). For avoiding these charges, the member on whom the expectation of facilitating the adherence of fair terms has been placed are not required to make immediate detailed offers which are construed in isolation from negotiation and discussion, which could fulfil the criteria of fairness led by lord Hoffmann. It was stated by the court that Nassar had the right to expect a reasonable approach towards a negotiated exist. However, Nassar deliberately chose not to negotiate on reasonable terms of withdrawal. This did not deny the fact that the management was indulged in oppressive conduct. So, not only were there shortcomings in the conduct of the plaintiff also, there was an absence of oppressive conduct in the view of the court after they considered the events which took place in formation of the three companies in which the common directors were present, and the events which took place in late 20007, 2008 and 2009 (Jade, 2009). And yet the directors failed in their directors duties as the court held that the winding up of the company was a just and equitable thing to do, owing to the application made by Nassar pursuant to section 461(I). The directors not only owe a duty of care to the shareholders, but also towards each other. They have a duty to work mutually and with a level of trust towards each other. The breach of this very duty on part of the directors led to the court making a winding up order (Jade, 2009). Decision of Court The court in this case had held that in this case, there had been no breach of section 232 and section 233 which relates to oppressive conduct on part of the management (Australasian Legal Information Institute, 2009b). The provisions of section 232 provides that in case the management of the company indulges in unfairly discriminatory, prejudicial or oppressive conduct, then pursuant to section 233, the court can pass an order to ask for the purchase of shares of the minority shareholder, to windup the company, to ask a director to do something or to refrain from doing something and the like (ICNL, 2017). However, for this, section 232 has to be fulfilled. However, the claims of plaintiff fell short on proving this. Had this been successful, the Oliveira and Grasso would have been ordered pursuant to section 233 to purchase the shares of Nassar. As the plaintiff failed in showing that the conduct was oppressive, there was no possibility of the court making an order under section 233 (Jade, 2009). The court in this accepted that by forming their companies, the three participants of this case had the entitlement and the expectation to participate in the daily management of the company. In the views of the court, these three were in such a position owing to the nature and the informality which attended the daily relationships, where there was a need for them to have a level of trust and mutual co-operation. The submission which was made by the three individuals, i.e., between Nassar, Grasso and Oliveira, in this case that they were partners was not accepted by the court. However, there relationship was such where there was a need of certain level of trust and mutual co-operation. The court also stated that they came to be associated together in a form which can be only deemed as quasi-partnership (BRI Ferrier, 2015). However, in this case, the parties had differences which could not be reconciled and due to these reasons, they did not participate in the daily activities of the company, requiring the quasi partnership to end. Considering it as a just and equitable thing to do, the court thus made a winding up order in this case and accepted that winding up, was the typical remedy which could be applied in the situation which was present, in which a working relationship which required trust, confidence and mutual co-operation was shattered. In order to come to the conclusion regarding the exclusion from the daily management of Nassar, the court referred to the breach of understanding regarding the participation of Nassar in the management. The participation had continued till it was abruptly ended in Nov 2007. And in the days to follow, Nassar stopped being active in the management of the company. And this is one of the reasons why Nassar failed to indulge in talks with Grasso and Oliveira, where t he matter could have been resolved with ease (Jade, 2009). As the counsel of both Grasso and Oliveira accepted that this was a classic case for a winding up order to be made on the grounds of the irretrievable breakdown in the relationship which was present between the members, the making up of a winding up order was deemed as a justified thing to do. For coming to this decision, a reference was made to Accurate Financial Consultants Pty Ltd v Koko Black Pty Ltd [2008] VSCA 86; (2008) 66 ACSR 325, where it was stated that winding up is a remedy for such cases where the trust, confidence and mutual co-operation breaks down. This is because equity is not an ordinary order for continuing with the association where the same is futility, and would need a constant supervision; further it would require specific enforcement of personal services. The court, after analysing the case, thus passed an order for the IPG and DGN to be wound up and appointed liquidators for both the companies (Jade, 2009). Impact of Decision This case acts as a key guidance for all the companies in the nation as it presents to them the case where a claim of oppression and mismanagement would fail. This case also clarifies that in such cases where there is a deadlock in the management and there is a breakdown in the corporate relations, the winding up of the company is deemed as a just and equitable thing to do. This power has been aptly given the courts pursuant to section 461(1)(k) of this act (WIPO, 2015). Hence, instead of making a claim of oppressive conduct, or any other matter, the shareholders of the companies could opt for this section and save both time and efforts of the court. Conclusion The case of Nassar v Innovative Precasters Group Pty Ltd highlights the complexities which the companies have to face and the manner in which the company can be wound up, when it is deemed as a just and equitable thing to do, even absence of oppressive conduct of the management. This case highlighted the failure on part of Nassar in showing that there had been an incident of oppressive, unfairly prejudicial or unfairly discriminatory conduct, merely because of a deadlock between the management of the company. The directors of the companies not only owe a duty of care towards the shareholders but also towards each other. However, this is not a statutory duty and a commonlaw duty. The only statutory duty which could be applied in this case was the duty of best interest. As the directors failed to come together and work for the company, this duty could be deemed to have been contravened. However, the decision which was made in this case was related to the winding up of the company as th is was deemed as a just and equitable thing to do. References Australasian Legal Information Institute. (2009a) Nassar v Innovative Precasters Group Pty Ltd [2009] NSWSC 342 (1 May 2009). [Online] Australasian Legal Information Institute. Available from https://www.austlii.edu.au/cgi-bin/viewdoc/au/cases/nsw/NSWSC/2009/342.html?context=1;query=Nassar%20v%20Innovative%20Precasters%20Group%20Pty%20Ltd [Accessed on: 07/09/17] Australasian Legal Information Institute. (2009b) Nassar v Innovative Precasters Group Pty Ltd [2009] NSWSC 513 (10 June 2009). [Online] Australasian Legal Information Institute. Available from: https://www.austlii.edu.au/cgi-bin/viewdoc/au/cases/nsw/NSWSC/2009/513.html?context=1;query=Nassar%20v%20Innovative%20Precasters%20Group%20Pty%20Ltd [Accessed on: 07/09/17] Australasian Legal Information Institute. (2017) Corporations Act 2001. [Online] Australasian Legal Information Institute. Available from: https://www.austlii.edu.au/au/legis/cth/consol_act/ca2001172/ [Accessed on: 07/09/17] BRI Ferrier. (2015) Breakdown in corporate relations: winding up on the just and equitable ground. [Online] BRI Ferrier. Available from: https://briferrier.com.au/news/breakdown-in-corporate-relations-winding-up-on-the-just-and-equitable-ground [Accessed on: 07/09/17] Cassidy, J. (2006) Concise Corporations Law. 5th ed. NSW: The Federation Press. Chamberlains. (2017) Winding up on just and equitable grounds: quasi-partnerships. [Online] Chamberlains. Available from: https://www.chamberlains.com.au/winding-up-on-just-and-equitable-grounds-quasi-partnerships/ [Accessed on: 07/09/17] Easton, M. (2013) Dont forget minority shareholders. [Online] Australian Institute of Company Directors. Available from https://www.austlii.edu.au/cgi-bin/viewdoc/au/cases/nsw/NSWSC/2009/342.html?context=1;query=Nassar%20v%20Innovative%20Precasters%20Group%20Pty%20Ltd [Accessed on: 07/09/17] Federal Register of Legislation. (2017) Corporations Act 2001. [Online] Australian Government. Available from: https://www.legislation.gov.au/Details/C2013C00605 [Accessed on: 07/09/17] ICNL. (2017) Corporations Act 2001. [Online] ICNL. Available from: https://www.icnl.org/research/library/files/Australia/Corps2001Vol4WD02.pdf [Accessed on: 07/09/17] Jade. (2009) Nassar v Innovative Precasters Group Pty Ltd [2009] NSWSC 342. [Online] Jade. Available from: https://jade.io/article/92998 [Accessed on: 07/09/17] Latimer, P. (2012) Australian Business Law 2012. 31st ed. Sydney, NSW: CCH Australia Limited. McInerney, A. (2015) Anthony McInerney SC. [Online] New Chambers. Available from: https://www.newchambers.com.au/wp-content/uploads/2015/04/McInerney-CV-update-February-2017.pdf [Accessed on: 07/09/17] Paolini, A. (2014) Research Handbook on Directors Duties. Northampton, MA, USA: Edward Elgar. WIPO. (2015) Corporations Act 2001. [Online] WIPO. Available from: https://www.wipo.int/wipolex/en/text.jsp?file_id=370817 [Accessed on: 07/09/17]