Publications by Amber Ferger
DATA 605 - Final Exam
Problem 1 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 \(\mu = \sigma = \frac{N+1}{2}\). set.seed(124) n <- 10000 N <- 1...
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DATA 605 - Week 16 Discussion
Exercises 14.2, Problem 5 (pg. 858) Sketch the given vector field over the rectangle with opposite corners \((−2,−2)\) and \((2,2)\), sketching one vector for every point with integer coordinates (i.e., at \((0,0),(1,2)\),etc.). \[\vec{F} = <x,0>\] First, let’s set up our grid of values. We will expand the grid so that we can graph our vec...
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DATA 605 - Assignment 14
Work out the Taylor Series Expansion for the following functions. For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. For each of the following, we will assume that each function is analytic (can be represented by a power series) and use the fact that a Taylor Series Expa...
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DATA 605 - Week 15 Discussion
Exercises 8.8, Problem 21 (pg. 496) Write out the first 5 terms of the Binomial series with the given \(k-value\): \(k = \frac{1}{2}\) Solution We know that the Binomial Series can be written as: \[(1+x)^k = \sum_{n=0}^{\infty} \binom{k}{n} x^n = 1 + kx + \frac{k(k-1)}{2!}x^2 + \frac{k(k-1)(k-2)}{3!}x^3 + \frac{k(k-1)(k-2)(k-3)}{4!}x^3 + ...\] W...
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DATA 605 - Assignment 13
Problem 1 Use integration by substitution to solve the integral below. \[\int 4e^{-7x}dx\] Solution Let \(u=-7x\) and \(du = -7dx\). Therefore, \(4dx = -\frac{4}{7}du\). By \(u\) substitution: \[\int -\frac{4}{7}e^{u}dx\] \[-\frac{4}{7} \int e^{u}dx\] \[-\frac{4}{7} e^{u} + C\] Substituting back in for \(u\), we get: \[-\frac{4}{7} e^{-7x} + C\...
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DATA 605 - Assignment 12
Data Description The attached who.csv dataset contains real-world data from 2008. The variables included are: \(Country\): name of country \(LifeExp\): average life expectancy for the country in years \(InfantSurvival\): proportion of those surviving to one year or more \(Under5Survival\): proportion of those surviving to five years or more \(T...
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DATA 605 - Week 13 Discussion
Chapters 4 - 6: Linear Regression Using R Question 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...
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DATA 605 - Assignment 11
Problem Using the cars dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) Solution Data Specs The cars dataset contains \(50\) rows and \(2\) columns. The explanatory variable will be speed...
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DATA 605 - Assignment 10
Problem Smith is in jail and has $1; he can get out on bail if he has $8. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability 0.4 and loses A dollars with probability 0.6. Find the probability that he wins $8 before losing all of his money if: he bets $1 each time (timid strategy) he bets...
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DATA 605 - Week 10 Discussion
Chapter 11: Markov Chains, Question 11 (pg.414) Question Assume that a man’s profession can be classified as professional, skilled laborer, or unskilled laborer. Assume that, of the sons of professional men, 80 percent are professional, 10 percent are skilled laborers, and 10 percent are unskilled laborers. In the case of sons of skilled labor...
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