Publications by Susanna Wong
DATA 605 Homework 14
Assignment Prompt This week, we’ll work out some Taylor Series expansions of popular functions. • \(f (x) = \frac{1}{1-x}\) • \(f (x) = e^x\) • \(f (x) = ln(1 + x)\) • \(f(x)=x^{1/2}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. The formula for Taylor Seri...
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DATA 605 Discussion 14
In Exercises 25 – 30, use the Taylor series given in Key Idea 8.8.1 to create the Taylor series of the given functions. Question 30 \(f(x)=(1+x)^\frac{1}{2}\cdot cos(x)\) (only find the first 4 terms) Function and Series First Few Terms \((1+x)^k=\sum_{n=1}^{\infty}\frac{k(k-1)\cdots (k-(n-1))}{n!}x^n\) \(1+kx+\frac{k(k-1)}{2!}x^2+ \cdots\) \...
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DATA 605 Homework 13
Question 1 Use integration by substitution to solve the integral below. \[\int 4e^{-7x} dx\] Let \(u = -7x\) \(\frac{du}{dx}=-7\) —> Solving for \(dx\). \(dx = -\frac{1}{7}du\) \(\int 4e^{-7x} dx\) \(=\int 4e^{u} \cdot \left (-\frac{1}{7}du \right )\) \(= -\frac{4}{7}\int e^{u} du\) \(= -\frac{4}{7} e^{u}\) where \(u = -7x\) \(= -\frac{4}{7} e^{-...
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DATA 605 Discussion 13
Question 18 Find the total area enclosed by the functons f and g. \(f(x)=-x^3+5x^2+2x+1\) \(g(x)=3x^2+x+3\) Plot the functions Based on the graph below, there are two areas enclosed by the function. library(ggplot2) x_values <- seq(-2,3, by = 0.1) f <- function(x) -x^3 + 5*x^2 +2*x+1 g <- function(x) 3*x^2+x+3 data <- data.frame(x = x_values, f...
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DATA 605 Discussion 12
Dataset The dataset are related to red wine of Portuguese “Vinho Verde” wine. Can we predict the wine quality based on the characteristics provided in the dataset? library(DT) data <- read.csv("https://raw.githubusercontent.com/suswong/DATA-605/main/winequality-red.csv", head = TRUE, sep=";") datatable(data, options = list(scrollX = TRUE)) Pac...
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DATA 605 Homework 12
Assignment The dataset for this assignment contains real-world data from 2008. Using the dataset answer the following questions: Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error,and p-values only. Discuss whether the assumptions of...
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DATA 605 Homework 11
Assignment Prompt 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.) library(ggplot2) library(DT) Dataset ?cars datatable(cars, options = list(scrollX = TRUE)) summary(car...
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DATA 605 Discussion 11
Dataset from R There are over 1000 dataset available in R. We can find some of the dataset in the following link: https://vincentarelbundock.github.io/Rdatasets/datasets.html For this week’s discussion, the dataset “Prestige” will be used to build a regression. Prestige of Canadian Occupations library(car) ## Loading required package: carDat...
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DATA 605 Homework 10
Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dollars with probability .6. Part A Find the probability that he wins 8 dollars before losing all of his money if he bets 1 dollar each time (tim...
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DATA 605 Homework 9
Problem 1 (Section 9.3 Exercise 11) The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by \(Y_{n}\) on the \(n\)th day of the year. Finn observes that the differences \(X_{n}=Y_{n+1}-Y_{n}\) appear to be independent random variables with a common distribution having mean \(\mu=0\) and variance \(\sigma^2=\f...
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