How to Prove the Complement Rule in Probability

Several theorems in probability can be deduced from the axioms of probability. These theorems can be applied to calculate probabilities that we may desire to know. One such result is known as the complement rule. This statement allows us to calculate the probability of an event A by knowing the probability of the complement AC. After stating the complement rule, we will see how this result can be proved. The Complement Rule The complement of the event A is denoted by AC. The complement of A is the set of all elements in the universal set, or sample space S, that are not elements of the set A. The complement rule is expressed by the following equation: P(AC) 1 – P(A) Here we see that the probability of an event and the probability of its complement must sum to 1. Proof of the Complement Rule To prove the complement rule, we begin with the axioms of probability. These statements are assumed without proof. We will see that they can be systematically used to prove our statement concerning the probability of the complement of an event. The first axiom of probability is that the probability of any event is a nonnegative real number.The second axiom of probability is that the probability of the entire sample space S is one. Symbolically we write P(S) 1.The third axiom of probability states that If A and B are mutually exclusive ( meaning that they have an empty intersection), then we state the probability of the union of these events as P(A U B ) P(A) P(B). For the complement rule, we will not need to use the first axiom in the list above. To prove our statement we consider the events Aand AC. From set theory, we know that these two sets have empty intersection. This is because an element cannot simultaneously be in both A and not in A. Since there is an empty intersection, these two sets are mutually exclusive. The union of the two events A and AC are also important. These constitute exhaustive events, meaning that the union of these events is all of the sample space S. These facts, combined with the axioms give us the equation 1 P(S) P(A U AC) P(A) P(AC) . The first equality is due to the second probability axiom. The second equality is because the events A and AC are exhaustive. The third equality is because of the third probability axiom. The above equation can be rearranged into the form that we stated above. All that we must do is subtract the probability of A from both sides of the equation. Thus 1 P(A) P(AC) becomes the equation P(AC) 1 – P(A). Of course, we could also express the rule by stating that: P(A) 1 – P(AC). All three of these equations are equivalent ways of saying the same thing. We see from this proof how just two axioms and some set theory go a long way to help us prove new statements concerning probability.

Comparing and Contrasting the Monsters of Beowulf with...

In any classic story about heroes and villains, the monsters involved are often characterized as the evil ones and, consequently, receive no justice under the law. Throughout the epic story Beowulf, the hero of the story encounters three monsters that are threats to society: Grendel, Grendel’s mother, and the dragon. The monsters in Beowulf are quickly targeted and destroyed because of the harm they cause to society. However, upon further examination of the monsters and the motives for their actions, the reader can view the monsters not as the cutthroat villains they may initially appear to be, but perhaps as victims of society. In today’s society, murderers and robbers are also portrayed as â€Å"monsters† because of the atrocious†¦show more content†¦On the other hand, Grendel, a creature who dwells in the swamplands away from human society, is treated as an outcast because of his lineage and relationship to â€Å"Cain’s clan, whom the creator had outlawed and condemned as outcasts† (ln. 106-107). Grendel has neither wealth, fame, nor honor; the fact that he does not even have a father to identify him makes him that much more worthless in society’s eyes, because the lack of a father downgrades one’s status. At a time when a person was identified by his or her paternal ancestry, fatherless Grendel roamed around aimlessly with no self-identity. Grendel was born completely devoid of distinction. To be fair, it is not Grendel’s fault that he is an outcast. He has no control over being one of the â€Å"fatherless creatures, [whose] whole ancestry is hidden in a past of demons and ghosts† (ln. 1355-1357). Yet it is because of this one unchangeable element, his birth into Cain’s clan, that Grendel is looked down upon by society. For this reason, Grendel’s natural-born characteristics eventually lead to his own destruction. Just as Grendel’s social status precludes his being shunned from society, so today is society’s relationship to wealth and social status significant in determining criminality within a population. The 2008 National Crime Victimization Survey (NCVS) stated that â€Å"[i]n

HR Planning and HR Management of the Company Sample for Students

Question: Discuss about the HR Planning and HR Management of the Company. Answer: Introduction This essay is based on the strategic HR planning and HR managementt of the company. It explains the relationship between the SHRM planning and HRM planning of the organisation. It explains the impact of HRM issues like diversity; high turnover rate and tight labour market influence the strategic position of the company. Furthermore, it also gives the solutions to overcome these issues significantly. Besides this, it also illustrates the real example of train failure case due to a shortage of drivers in Queensland. Australia. It also explains the various reasons behind the project failure like communication issues, shortage of resources on time, lack of information and rigid bureaucratic structure makes the incident happened. Lastly, in this report, it also explains the importance of a resource-based approach to the company. It will help the HR department to plan their resources effectively so that the objectives of the company in a precise manner. Strategic HR Planning Human resource department is an important functional department of any company. The systematic human resource planning helps the company to optimise the resources significantly and makes the organisation competitive in the marketplace. The role of human resource planning is to review the periodical requirements of the company i.e. need of skilled and knowledgeable employees are available at the time of requirement in the company. Human resource planning is linked with the organisational strategy to ensure that the requirement of the talent resource is fulfilled, the cost of the labour is controlled, the requirement of staff is appropriate and skilled employees are retained in the company (UF, 2016). The human resource simultaneously works with the line managers to ensure all above-given requirements are fulfilled well. Effective human resource planning helps the company to increase the productivity of the company. It includes below steps Figure 1: (Source: UF, 2016) HR Planning Above figure indicated the process of HR planning in an organisation to achieve its long and short term goals. On the other side, Strategic human resource planning focus on recruitment, selection, training and development, payroll management, performance appraisals and Grievances in the company. Human resource planning analyses the demand and supply of the human capital in the market to evaluate the internal and external factors of the organisation. Internal factors include organisational, technological and political changes in the company and external factors like demographic, environmental and social changes in the market (AZcentral, 2016). Strategic human resources planning assesses through SWOT analysis to manage the resources to enhance the capability and competitiveness of the organisation. Strengths -Skilled employees -Leadership and top management -Knowledge and Expertise -Organizational policies -Organization environment Weaknesses -Low employee morale -High turnover -Remuneration and compensation -Budget constraints Opportunities -New markets -Innovative ideas and talented workforce -Increased demand for products and services Threats -Increased competition -Wages and benefits Strategic human resource planning considers all the internal and external factors of the organisation through above SWOT analysis and makes the organisation competitive. In the todays globalisation era company faces the many challenges and issues regarding high turnover, tight labour market, skills shortage, ageing population and diversity. The company can be strategic and competitive if the HR department efficiently works on the particular issues. The issue related to high employee turnover rate is reduced by the following factors to be considering which is shown below. Remuneration and compensation should be attractive and it can be revised periodically according to the performance of the employees HR department should develop the flexible growth model in the company for employees to gives more growth and development. Appreciation and recognition programs help employees to motivate in their work and it reduces the employee turnover rate in the company (SHRM, 2016). The company faces the issue of tight labour market due to increase in offshore activities and globalisation at the workplace. The effect of free trade agreement between some of the countries like China, Australia, South Korea and Japan impacts the trading systems and influence the international labour market at the global level. In tight labour conditions, HR department should offer the competitive packages and remuneration to the employees while recruitment. Moreover, the company needs to improve the area of their recruitment criteria. For instance, the company should hire people who dont even fulfil all the job requirements initially and train them later when they join the company. This method helps to improve the recruitment level at the time of tight labour conditions (SBS, 2016). The skills shortage is also a major issue in the company that decreases its competitiveness in the market. The company can recruit the new candidates those who are more creative, hard worker and fit wit h the companys culture. Internal Training programs strength the skills they need for the job. The company can manage the ageing population through more investments in their training, development and learning process so they can give the positive results to the company. The company needs to reform its pension and health policies systems to meet the needs of the older people. Also, the company can better use of existing resources and adoption of advanced technology to make employee healthy, active and more productive in the company (Bloom, et al., 2011). Lastly, Diversity is also a major issue which is faced by the company.HR department should provide training and education programs to the employees regarding diversity so that they can understand and respect the differences of culture, race and language. Supporting and promotes diversity programs helps to increase the outcomes of the company and become more competent at the workplace. HR Planning and Project Management Human resource planning is an important resource on the project. The company needs to plan effectively their human resource to accomplish projects on time. The human resource planning includes the roles and responsibilities of team members, project organisation charts and staffing management. The objective of the human resource plan is to ensure that required human capital is a recruit and effectively train and develop according to the project requirements so that they can effectively manage their assigned responsibilities and perform better (PMD, 2017). As per the article is given in the problem, it is analysed that the problems were arisen due to lack of resources for the particular service. The drivers are not available for the train in their peak hours in Queensland Australia. Another issue is identified from the article is the lack of communication differences in the department of the team members makes the incident worse. As per the article, it indicates that someone in the team knew that the problem would occur and it was not communicated on time (News, 2016).Lastly, the interim timetable of the railway not updated on time that will create the problem for the staff and customers to makes this incident happened. It can be said that the lack of information or late project information affects the project significantly. As per the incident, it clearly depicts that lack of HR planning makes the incident occurred.HR planning is very important part of project management to deliver the projects successfully. In this situation, the fir st thing is a lack of resources available to continue the activity. The drivers were not available at peak hours of trains. Another factor related to the HR planning is the lack of communication among the team members makes the situation difficult for the whole team and it also hampers the activities of the project. In this case it is identified that someone in the team is known that the incident would occur but they didnt inform the top management or subordinates about the problem (IPLA, 2016). Timely communication reduces the difficulties in the project and it cannot be disastrous for the management. Lastly, lack of information and clear direction puts the project in difficult conditions. For this situation, employees dont have clear instructions and effective communication flow among the team members to handles the situation well. Similarly, project failure influences political factors. From this incident, the government cancelled the project's contracts and would change the HR policies that involves more responsible people are involved in handling the critical activities. The failure of project activities directly influences the politicians and its responsibility area. In this incident, it can be identified that lack of communication, lack of transparency in the political system and lack of information makes this incident happened. Lack of communication occurs as the junior level ministers not informed about the problem to the top management in a timely manner that indicates the transparency in the bureaucrat structure is not clear (HealthKnowledge, 2016). Moreover, it is also considered that timely information to the management leads to avoid this situation. Resource-based view (RBV) The resource-based view is a concept that says resources are medium for achieving better performance of the organization. It is also an approach for attaining competitive advantage, which occurred in 1980 and 1990. It also suggests that company should focus on itself to find competitive advantage resources rather than focusing on competitive environment for that (Lin and Wu, 2014). The figure below depicts resources based view along with its main aspects. There is optimistic association amongst performance of the organization and human capital. The stress on human resource capital in companies imitates vision that market value relies fewer on physical resources, but rather on insubstantial ones, predominantly human resources. The RBV highlights the significant position of human resource capital in attaining results of organisation (Ologbo, Oluwatosin and Okyere-Kwakye, 2012). The RBV set up the significance for the company in constructing a precious set of resources and collecting them simultaneously in an exclusive and vibrant manner to generate success of the company. In a genuine sense, Human capital is an imperceptible asset. The resource-based view of the company makes stronger the frequently recurring declarations from the region of strategic human resource management that most significant assets for the success of the company are people. It has established repeatedly that spending in the unremitting development of the capacitie s of the company is the solution for long-run success. Growing the companys people, the Human Capital is a speculation for the future of the company and that speculation should be delineated in the Human Resource plan for the company. Human resource planning is fitting as the strength for a money making company. Every company acknowledges the significance of human resource planning. To comprehend the HR planning it is said that it the procedure with the help of which administration assures that it has the accurate strategy or plan for their employees. Resource based view guides the company to understand the need of human resource planning (Oke, Walumbwa and Myers, 2012). It helps to know how important assets are employees. The employee makes an organisation different from one another. RBV helps the organization to attain high-performance administration, high-involvement administration and high-commitment administration. Human resource tactics are the imperative constituent to the business tactics and critical aspect of the resource based. With the guidance of RBV, the company can construct the efficient HR planning, as RBV makes to understand each aspect of human capital, its importance, its working, its effective ness, its need, etc. Conclusion As per the above essay, it finds that strategic human resource planning is the crucial part of the company operations. The strategic human resource planning helps the company to focus on the main activities of the company like recruiting, selection, training and development and appraisals. Whereas, Human resource planning addresses the long-term issues like demand and supply of the workforce and ensures that it comes under the budget of the company. Moreover, it also finds from the above essay that proper human resource management of the company addresses the issues like diversity, high turnover, tight labour market and ageing population. Furthermore, in this essay, it reflects the real incident of train cancellation in Queensland, Australia due to a shortage of resources and lack of timely information availability to the senior officials cause the worst incident. Moreover, it also depicts that Resource Based View approach is more important for the company to assign their resources e ffectively. From the various issues listed in the above essay, it concludes that strategic human resource planning is important in every company to deliver its objectives significantly. Furthermore, it also concludes that proper training and development programs and policies helps the company more strategic and overcome the issues like diversity high turnover and tight labour markets. Finally, it concludes that availability of resources, transparent information and flexible bureaucratic structure reduces the chance of accidents in projects. References Az Central (2017) Human Resource SWOT Analysis. [Online].Available at: https://yourbusiness.azcentral.com/human-resource-swot-analysis-1288.html (Accessed: 29th March 2017) Bloom, D.E., Boersch-Supan, A., McGee, P. and Seike, A., (2011) Population aging: facts, challenges, and responses.Benefits and compensation International,41(1), p.22. HealthKnowledge (2016) Assessing the impact of political, economic, socio-cultural, environmental and other external influences.[Online].Available at: https://www.healthknowledge.org.uk/public-health-textbook/organisation-management/5b-understanding-ofs/assessing-impact-external-influences (Accessed: 29th March 2017) IPLA (2016) Why Projects Fail. [Online]. Avaialble at: https://calleam.com/WTPF/?page_id=2213 (Accessed: 29th March 2017) Lin, Y. and Wu, L.Y. (2014) Exploring the role of dynamic capabilities in firm performance under the resource-based view framework, Journal of business research, 67(3), pp. 407-413. News (2016) Queensland Rail disruptions: Annastacia Palaszczuk 'furious' over 100 cancelled trains in Brisbane. Available at: https://www.abc.net.au/news/2016-10-23/annastacia-palaszczuk-furious-over-queensland-rail-disruptions/7957862 (Accessed: 29th March 2017) Oke, A., Walumbwa, F.O. and Myers, A. (2012) Innovation strategy, human resource policy, and firms' revenue growth: The roles of environmental uncertainty and innovation performance, Decision Sciences, 43(2), pp. 273-302. Ologbo, A.C., Oluwatosin, O.S. and Okyere-Kwakye, E. (2012) Strategic Management Theories and the Linkage with Firm Competitive Advantage from the Human Resource-Based View, International Journal of Research in Management Technology, 2(4), pp. 366-376. PMD (2016) Human Resource Plan. [Online]. Available at: https://www.projectmanagementdocs.com/project-planning-templates/human-resource-plan.html#axzz4chUeqIYK (Accessed: 29th March 2017) SBS (2017) Five ways companies can address a shortage of skills. [Online] . Available at: https://www.theglobeandmail.com/report-on-business/careers/careers-leadership/five-ways-companies-can-address-a-shortage-of-skills/article11616220/ (Accessed: 29th March 2017) Shrm (2016) Strategic-HRM. [Online].Available at: https://www.shrm.org/india/hr-topics-and-strategy/strategic-hrm/Pages/default.aspx (Accessed: 29th March 2017) UF (2016) Impact of Employee Turnover and Solutions to Help.[Online].Available at: https://essentialsofbusiness.ufexec.ufl.edu/resources/leadership/impact-of-employee-turnover-and-solutions-to-help/#.WNtGcNKGPDc (Accessed: 29th March 2017)

Odysseus Character Essays - Odyssey, Ancient Greek Religion

Odysseus Character The Odyssey is an epic poem, which revolves around Odysseus and his journey home from the war at Troy. Throughout his travels he is met with many obstacles and adventures. There are times when he thinks he will never make it home. But through perseverance, faith, maturation and heroics, he manages to survive and reach his homeland of Ithaca as a changed man. In The Odyssey, Odysseus, the main character must journey from Troy to his homeland of Ithaca. Throughout this journey he learns many lessons, faces obstacles testing his physical and mental strength and grows from an arrogant, self-centered hero into a humble, respectful survivor. With the help of the Gods he is finally able to return to Ithaca as an honorable man. In Book VI of the Odyssey, Odysseus wakes on the shore of Phaecia. The Goddess Athena has sent the beautiful Nausicaa a dream instructing her to wash clothes in preparation for an upcoming marriage. Athena makes Nausicaa brave and Odysseus handsome bringing them together in order to assist Odysseus to the house of the king. In this particular book the Gods assist Odysseus and he manages to come closer to getting home. Athena helps him out over and over again in Book VI. Everything seems to be done to help Odysseus and so he is lucky to have the Gods behind him. "but the grey-eyed Goddess Athena made her tarry, so Odysseus might behold her beauty and win her guidance to the town" (175). Here Odysseus is actually being led where he needs to go by Athena indirectly. All the places with lush greenery and the resting-place of Odysseus has even been made by Athena. "The sun was going down when they went by Athena's grove" (181). The manipulation by the Gods appears to lead t a common goal, the survival of Odysseus and the assistance of getting him home. The gods may not be able to stop fate but they help Odysseus learn to use their guidance to his advantage for his survival. In Book VIII, King Alkinoos calls an assembly asking the Phaeacians to help Odysseus. During this meeting there is competition to entertain Odysseus. After being insulted by one of the Phaeacians, ""The reason being, as I see it, friend, you never learned a sport, and have no skill in any of the contests of fighting men" (185). With that, Odysseus throws a discus farther than anyone ever has. "Anyone else for an edge for competition try me now" (186) This proves Odysseus has a problem with his pride. Although this pride does help him throughout his journey, he uses it here as a vice to show others his greatness. His arrogance really shows through here. By insulting his abilities, Phaeacians insulted his manhood and he defended it to the highest degree. In Book IX, Odysseus encounters the Kyklops and uses his cunningness and bravery to escape. Here we see a new side of Odysseus. First he vividly narrates his love for his home in this book. "I shall not see on earth a place more dear" (198). "Where shall a man find sweetness to surpass his own home and his parents (198)? Odysseus seems able to survive by using all his energy to find his way home. He uses this energy in his plot to get away from the Kyklops. His plan is both brave and ingenious. He tells the Kyklops his name is Nohbdy. Then after being blinded, Odysseus and his men are able to escape. The Kyklops yells to his friends, "Nohbdy, Nohbdy tricked me, Nohbdy's ruined me" (207)! With this, he gets no help and Odysseus is free. However again his pride gets the best of him for as they are escaping he yells, "If ever a mortal man inquire how you were put to shame and blinded, tell them Odysseus, raider of cities, took your eye" (210). This again proves to hurt Odysseus and makes his journey more difficult. His foolishness proves to be a thorn in his side throughout The Odyssey. By revealing his name he sets himself up for the angry God Poseidon. In Book X, foolishness again causes Odysseus trouble. As his Odyssey seems almost over and the men are close to Ithaca, a sack of wind given to Odysseus by Aeolus is unleashed. This blows their ship all the way back to where they started. Odysseus then ends up with Kirke, daughter of the Sun. Kirke turns all the crewmates into pigs and lures Odysseus into her bed.