Mean of a log normal random variable: Theorem 1: Suppose Y = ln X is a normal distribution with mean m and variance v‚ then X has mean exp( m + v /2 ) Proof: The density function of Y= ln X Therefore the density function of X is given by Using the change of variable x = exp(y)‚ dx = exp(y) dy‚ We have = Note that the integral inside is just the density function of a normal random variable with mean (m-v) and variance v. By definition‚ the integral evaluates to be 1. Proof of Black Scholes
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ROP based on Normal Distribution of LT demand -Example No. 1 Example : Suppose that the manager of a construction supply house determined from historical records that demand for sand during leadtime averages 50 tons. In addition‚ suppose the manager determined that the demand during leadtime could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer the following questions‚ assuming that the manager is willing to accept a stockout risk of no
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Problem Sheet - I 1. Researcher conducted by a tobacco company indicates that the relative frequency distribution of tar content of its newly developed low-tar cigarette has a mean equal to 3.9 milligrams of tar per cigarette and a standard deviation equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true‚ what is the probability that the mean
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13. Variance and Standard Deviation (expected). Using the data from problem 13‚ calculate the variance and standard deviation of the three investments‚ stock‚ corporate bond‚ and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are correct‚ which investment would you choose considering both risk and return? Why? ANSWER Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2 + 0.50 x (0.04 – 0.033)2 + 0
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It’s Kind of a Funny Story Ned Vizzini Prompt #2 The word hope‚ in the dictionary means a feeling of expectation and desire for a certain thing to happen. Everyone finds hope in their own way. Things or events we may not see hope in‚ may just be the defining hopeful moment in someone else’s life. Hope is in our daily lives weather we choose to see it or not. It is in the books we read‚ the people we meet and in our lives as a hole. A famous quote by Desmond Tutu states ¨Hope is being able to see
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A population of measurements is approximately normally distributed with mean of 25 and a variance of 9. Find the probability that a measurement selected at random will be between 19 and 31. Solution: The values 19 and 31 must be transformed into the corresponding z values and then the area between the two z values found. Using the transformation formula from X to z (where µ = 25 and σ √9 = 3)‚ we have z19 = (19 – 25) / 3 = -2 and z31 = (31 - 25) / 3 = +2 From the area between z =±2 is 2(0
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STAT11-111 Business Statistics WEEK 3 and WEEK 4: WORKSHOPS ______________________________________________ This workshop is to be completed during Week 3 and Week 4 workshops and will depend on how quickly we get through the lecture material. Part A: Week 3 Exercise 4.2‚ Exercise 4.4. Exercise 4.5‚ Exercise 4.6‚ Exercise 4.7. Your tutor will discuss these 3 questions with you in the class. Exercise 4.8‚ Exercise 4.9. Exercise 4.10‚ Exercise 4.12‚ Exercise 4.14. Exercise 4.15‚ Exercise
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Assignment: Interpreting Correlational Findings Following are brief summaries of correlational findings‚ in which variables were found to be significantly associated with each other. Your task is to determine which of the three major causal models (i.e.‚ interpretations) could account for each finding. Indicate in the table below‚ by placing an X in the appropriate space‚ which of these three models could provide a possible explanation. Place an X in the space only if you judge the causal
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SECTION-B 5TH MARCH 2014 PERSONAL AND NATIONAL IDENTITIES IN “FUNNY BOY” In Shyam Selvadurai’s novel “Funny Boy”‚ a boy’s growth into adolescence is set against stringent heteronormative society and escalating political tensions in Sri Lanka. There is no watertight structure to say whether one’s national identity governs one’s personal identity or vice versa‚ or for that matter‚ that there is no difference between the two. The novel “Funny Boy” carefully traces questions of identity at the individual
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Mr. Braga ENG 2D0 Jun 1 2017 Arjie’s Self Discovery Growing up during a time of violent political upheaval in Sri Lanka‚ Arjie Chelvaratnam finds himself on an unexpected journey towards discovering his inner person. In Shyam Selvadurai’s Funny Boy‚ the author shows us the struggles and understanding the protagonist‚ Arjie‚ goes through‚ being homosexual‚ Tamil‚ and breaking gender roles/ stereotypes and not fitting society’s norms to discover his identity through isolation. Gender roles
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