Publications by Team : Omega (Mario Pena, Deepak Sharma, Ramnivas Singh)
Value At Risk DATA618
About This worksheet looks at VaR calculations for the two cases of single and multiple equity asset. We will also demonstrate VaR calculations for a fixed income investment. Task 1: VaR Calculations: Single Equity Asset Consider the time series of a stock of your choice (we looked at Fedex stock) and for the time-period from Jan 1, 2018 to pres...
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Final Project DATA605
Computational Mathematics Final Project Problem 1. Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to \(N\), where \(N\) can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of \(\mu =\sigma =\frac { N+1 }{ 2 }\) We w...
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Discussion 15 DATA605
Discussion 15 Chapter 12.5 Problem 7: In Exercises 7-12, functions \(z=f(x,y)\), \(x=g(t)\), and \(y=h(t)\) are given. Use the Multivariable Chain Rule to compute \(\frac { dz }{ dt }\). Evaluate \(\frac { dz }{ dt }\) at the indicated t-value. In our problem we are given: \(z=3x+4y\), \(x={ t }^{ 2 }\), \(y=2t\); \(t=1\) Following the Multivar...
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Discussion 13 DATA605
Discussion 13 Chapter 4.3 Problem 3: Find the maximum product of two numbers (not necessarily integers) that have a sum of 100. In this problem we realize that our two numbers will be \(x\) and \((100-x)\) in order to have a sum of 100, then our product will be \(P=x\times (100-x)\) or \(P=100x-{ x }^{ 2 }\) To find the two numbers that give us t...
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Discussion 12 DATA605
Discussion 12 Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? For this week’s discussion...
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Discussion 11 DATA605
Discussion 11 Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? For this week’s discussion, I used a dataset that I had previously worked with in my DATA606 course last semester. These data basically consist of college majors and information as it relates ...
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Discussion 10 DATA605
Discussion 10 Exercise 11.1 #4 For Example 11.6, find the probability that the grandson of a man from Harvard went to Harvard. Given the following Markov chain from the example: \(P=\begin{matrix} \begin{matrix} \\ H \end{matrix} \\ Y \\ D \end{matrix}\begin{matrix} H & Y & D \\ \begin{matrix} .8 \\ .3 \\ .2 \end{matrix} & \begin{matrix} .2 \\ .4...
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Discussion 9 DATA605
Discussion 9 Exercise 9.1 #14 A restaurant feeds 400 customers per day. On the average 20 percent of the customers order apple pie. (a) Give a range (called a 95 percent confidence interval) for the number of pieces of apple pie ordered on a given day such that you can be 95 percent sure that the actual number will fall in this range. A 95% confi...
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Discussion 8 DATA605
Discussion 8 Exercise 8.1 #1 A fair coin is tossed 100 times. The expected number of heads is 50, and the standard deviation for the number of heads is \({ (100\times 1/2\times 1/2) }^{ 1/2 }=5\). What does Chebyshev’s Inequality tell you about the probability that the number of heads that turn up deviates from the expected number 50 by three o...
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Discussion 7 DATA605
Discussion 7 Exercise 6.1 #8 A royal family has children until it has a boy or until it has three children, whichever comes first. Assume that each child is a boy with probability 1/2. Find the expected number of boys in this royal family and the expected number of girls. We will use the following general formula to find the expected number of bo...
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