Probability Distribution in Statistics

If you spend much time at all dealing with statistics, pretty soon you run into the phrase â€Å"probability distribution.† It is here that we really get to see how much the areas of probability and statistics overlap. Although this may sound like something technical, the phrase probability distribution is really just a way to talk about organizing a list of probabilities. A probability distribution is a function or rule that assigns probabilities to each value of a random variable. The distribution may in some cases be listed. In other cases, it is presented as a graph. Example Suppose that we roll two dice and then record the sum of the dice. Sums anywhere from two to 12 are possible. Each sum has a particular probability of occurring. We can simply list these as follows: The sum of 2 has a probability of 1/36The sum of 3 has a probability of 2/36The sum of 4 has a probability of 3/36The sum of 5 has a probability of 4/36The sum of 6 has a probability of 5/36The sum of 7 has a probability of 6/36The sum of 8 has a probability of 5/36The sum of 9 has a probability of 4/36The sum of 10 has a probability of 3/36The sum of 11 has a probability of 2/36The sum of 12 has a probability of 1/36 This list is a probability distribution for the probability experiment of rolling two dice. We can also consider the above as a probability distribution of the random variable defined by looking at the sum of the two dice. Graph A probability distribution can be graphed, and sometimes this helps to show us features of the distribution that were not apparent from just reading the list of probabilities. The random variable is plotted along the x-axis, and the corresponding probability is plotted along the y-axis. For a discrete random variable, we will have a histogram. For a continuous random variable, we will have the inside of a smooth curve. The rules of probability are still in effect, and they manifest themselves in a few ways. Since probabilities are greater than or equal to zero, the graph of a probability distribution must have y-coordinates that are nonnegative. Another feature of probabilities, namely that one is the maximum that the probability of an event can be, shows up in another way. Area Probability The graph of a probability distribution is constructed in such a way that areas represent probabilities. For a discrete probability distribution, we are really just calculating the areas of rectangles. In the graph above, the areas of the three bars corresponding to four, five and six correspond to the probability that the sum of our dice is four, five or six. The areas of all of the bars add up to a total of one. In the standard normal distribution or bell curve, we have a similar situation. The area under the curve between two z values corresponds to the probability that our variable falls between those two values. For example, the area under the bell curve for -1 z. Important Distributions There are literally infinitely many probability distributions. A list of some of the more important distributions follows: Binomial distribution – Gives the number of successes for a series of independent experiments with two outcomesChi-square distribution – For use of determining how close observed quantities fit a proposed modelF-distribution – Used in the analysis of variance (ANOVA)Normal distribution – Called the bell curve and is found throughout statistics.Student’s t distribution – For use with small sample sizes from a normal distribution

Strategies for Presenting Content in the Classroom

Week 3 Quiz World Cultures 2 Essay - 1575 Words

User | Allis Faye Luster | Course | World Cultures II | Test | Week 3 Quiz | Started | 7/17/13 9:53 PM | Submitted | 7/18/13 1:32 AM | Status | Completed | Attempt Score | 72 out of 80 points | Time Elapsed | 3 hours, 39 minutes out of 4 hours and 30 minutes. | Instructions | | Question 1 2 out of 2 points | Why did Gabrieli organize his compositions around a single note-the tonic note? Answer | | Selected Answer: | To heighten the sense of harmonic drama | Correct Answer: | To heighten the sense of harmonic drama | | | Question 2 2 out of 2 points | Why did the Baroque artists place†¦show more content†¦Answer | | Selected Answer: | To symbolize worldly wealth, vanity, and mortality | Correct Answer: | To symbolize worldly wealth, vanity, and mortality | | | Question 15 2 out of 2 points | According to Francis Bacon, what were the greatest obstacles to human understanding? Answer | | Selected Answer: | Superstition and religion | Correct Answer: | Superstition and religion | | | Question 16 2 out of 2 points | Why were the Catholic and the Protestant Churches opposed to Keplers and Galileos heliocentric theory? Answer | | Selected Answer: | For contradicting certain biblical passages | Correct Answer: | For contradicting certain biblical passages | | | Question 17 2 out of 2 points | In The Little Street why does Vermeer include a half-whitewashed wall and a mortar-filled cracked faà §ade? Answer | | Selected Answer: | To show the tensions of domestic life | Correct Answer: | To show the tensions of domestic life | | | Question 18 2 out of 2Show MoreRelatedYolo1583 Words   |  7 PagesSciences San Beda College COURSESYLLABUS First Semester, AY2014-2015 San Beda College, a Catholic educational institution, is committed to the Christian formation of the Bedan Community as its service to the Church, the Philippine society, and the world. 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Research Methodologies Human Factors Influencing

Question: Describe about the Research Methodologies for Human Factors Influencing. Answer: Part A Review of Article 1 Mr. Chandrakantan Subramaniam has published this article. In this article of Human factors influencing fire safety measures, he has stated about the fire incidents and relating facts regarding the fire safety measures that have been affected by the factors of the human society. He had taken the evidence of several incidents of fire safety in the duration of recent years. For this reason, Chandrakantan Subramaniam had conducted a study in support of the article in the schools of Malaysia which has been included the Ministry of Education. The study is conducted because of the founding of the fire outbreaks in the schools and institutions of Malaysia (Subramaniam, 2004). These fire outbreaks occurred in 22 schools of primary and secondary division along with the higher institutions in the year 1999 where a number of losses have been recorded to be of RM 534,400. The author of this article basically intended to focus on the identification of the conditions of fire safety in the residenti al colleges of that has been situated in the local universities of Malaysia. Due to the ongoing of the study, there has been an approach of the audit introduced including various questionnaires, which is mostly done to make the collection of the primary data carry out the research (Subramaniam, 2004). Then after the primary data collection and audit process, the results have shown that the level of compliances of the overall condition of fire safety can be said to have 76%. Therefore the researches or the surveys have been shown that there have been some predisposing factors for this condition of fire safety that includes the knowledge, attitude, and belief and along with that having somehow positive attitude towards the safety behaviour of the organizations along with other important six points on fire safety issues. Review of Article 2 This article Exploring the Drivers of Inter organizational Relationship Magnitude has been published by Susan L. Golicic and John T. Mentzer, had explained regarding the exploration of drivers that are mediating the magnitude of the relationship between the organizations in the global market (Golicic Mentzer, 2005). The study has come with the portfolio of the types of investments of the firm which has been surround by the suppliers, and the customers that too be bonded with various types of relationships and the magnitude of that relationship is only studied in this matter. The authors have mentioned about the structure of the relationship in this matter that has shown the breaking down the components of the relationship to be the magnitude and the type (Golicic Mentzer, 2005). The study has shown the distinction between the two that can be said to have an important to set out the theories and practices of the inter-organizational relationships by which it will able to gain more s upportive portfolio that will give the better understanding to the firm to manage the work. For this reason, there must have knowledge of the structure of the companys relationship along with its magnitude, which can be assumed to have the contribution in the relationship (Golicic Mentzer, 2005). Therefore the study has been done including the exploration and the expansion of the research for the contribution of the drivers in the process of influencing of the magnitude of the relationship. For this reason, the study came out with the findings of eight types of drivers, i.e., capabilities, external influence, history, importance, expected benefits, interpersonal interaction, performance along with the strategy congruence. Part B Strength and Weakness of Article 1 The research activities depicted in the two selected articles have to be reviewed especially in the context of the strengths and weaknesses of the research methodologies used by each of the research processes. The journal articles refer to research on the identification of the influencing factors behind the determination of the magnitude of relationships within organizations and the consideration of human factors which are crucial for instating fire safety measures (Subramaniam, 2004). The research methods utilized in each research activity can be considered as profound excerpts of the conventional aspects associated with research such as data collection and analysis methods. However, the most significant part of research activity is observed in the data analysis part which reflects on the content analysis. The scope of primary data collection could be considered as strength for the research as it enables the acquisition of relevant and comprehensive data about research topic. The use of primary data collection methods such as interviews, surveys, questionnaires and focus groups are meant for facilitating a flexible platform for interaction between the sample population and the researcher. The researchers first-hand interaction with the respondents results in derivation of credible information which would not be acquired through the secondary research or review of the literature. A collection of data from the ground level forms a crucial aspect of the research activity and hence primary data collection methods are preferred for the multitude of information generated from the process (Golicic Mentzer, 2005). Primary data collection is also associated with the advantages of data obtained which are clearly reflected in the comprehensiveness and diversity of data. The association of respon dents with varying technical proficiency could be reflected in the variety obtained in the primary data. However, the weaknesses of primary data collection could be observed in the structural definitions of various methods used for primary research. Strength and Weakness of Article 2 In Article 2, Secondary data collection is also a prominent entity in the selected research journals. The process of secondary research is characterized by the extraction of a comprehensive impression of the literature related to the research topic and the various research publications and academic work which reflect appropriately on the research issue. Furthermore, secondary research methods also help in the realization of minimal investment of resources especially in terms of finance (Subramaniam, 2004). The additional issues which could be reflected with regard to secondary research have to be realized in the context of the implications of negligence for relevant factors associated with research issue. The disadvantage of the secondary data collection is also observed in the diversity of the information which could not be collated flexibly according to the research issue. The use of content analysis, as well as coding system for representing the information obtained from the data collection methods, is also observed in the journal articles. The consideration of information coding is helpful in defining standard units for recording and storage of information as well as increasing the flexibility of research (Golicic Mentzer, 2005). However, the coding system could create additional ambiguities for the researcher without precise translation of the information stored in coded form. The profound strengths and weaknesses of the methods for content analysis adopted in the research articles provided could be thus validated. References Subramaniam, C., 2004. Human factors influencing fire safety measures. Disaster Prevention and Management: An International Journal,13(2), pp.110-116. Golicic, S.L. and Mentzer, J.T., 2005. Exploring the drivers of interorganizational relationship magnitude.Journal of Business Logistics,26(2), pp.47-71.