Publications by Kristin Lussi
DATA 605 Homework 14
Week 14 Homework 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. To calculate the expansions, we will use ...
3365 sym
DATA 605 Week 14 Discussion
Page 496 Exercise 27 Use the Taylor series given in Key Idea 8.8.1 to create the Taylor series of the given functions. \(f(x)=sin(2x+3)\) Solution using R library(pracma) f <- function(x) sin(2*x + 3) taylor_series <- taylor(f, 0) print(taylor_series) ## [1] 0.09407953 1.31998927 -0.28224001 -1.97998499 0.14112001 Solution by Hand Calcula...
818 sym R (167 sym/2 pcs)
DATA 605 Homework 13
Homework 13 Question 1 Use integration by substitution to solve the integral below. \[ \int 4e^{-7x}dx \] Solution \[ u = -7x \\ du = -7 dx \rightarrow \frac{-1}{7}du = dx\\ \int 4e^{-7x}dx \rightarrow \text{ Substitute } \rightarrow 4 \int e^u \frac{-1}{7} du\\ = \frac{-4}{7} \int e^u du = \frac{-4}{7} e^u + C \\ = \frac{-4}{7} e^{-7x} + C \] Q...
4000 sym
DATA 605 Week 13 Discussion
Page 395 #5 A 100 ft rope, weighing 0.1 lb/ft, hangs over the edge of a tall building. Part A Question How much work is done pulling the entire rope to the top of the building? Solution \[ 0 \leq x \leq 100\\ dW = \text{amount of work required to lift a segment of the rope a distance x from its current position} =0.1 x dx\\ x = \text{height}\\ ...
1129 sym
DATA 605 Homework 12
Import Data who_data <- read_csv(url, show_col_types = FALSE) head(who_data) ## # A tibble: 6 × 10 ## Country LifeExp InfantSurvival Under5Survival TBFree PropMD PropRN PersExp ## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 Afghanis… 42 0.835 0.743 0.998 2.29e-4 5.72e-4 ...
7415 sym Python (4950 sym/25 pcs) 11 img
DATA 605 Discussion Week 12
Medical Expenses In this analysis, I will be using the Insurance Premium Prediction dataset from Kaggle. I will determine which variables in the dataset are significant predictors of medical expenses by creating a multiple linear regression model. Import Data url <- "https://raw.githubusercontent.com/kristinlussi/DATA605/main/Week12/insurance.csv"...
3394 sym 5 img
DATA 605 Homework 11
Cars Analysis 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(dplyr) library(ggplot2) data(cars) Let’s take a glimpse of the data. head(cars) ## speed dist ##...
2648 sym R (2328 sym/12 pcs) 5 img
DATA 605 Week 11 Discussion
Introduction The dataset I will be working with is the Housing Prices Dataset from Kaggle. I will be creating a linear model that explains the relationship between area and housing price. Visualize the Data houses <- read.csv("https://raw.githubusercontent.com/kristinlussi/DATA605/main/WEEK11/Housing.csv") head(houses) ## price area bedrooms ...
2288 sym 5 img
DATA 605 Homework 10
Question 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. Find the probability that he wins 8 dollars before losing all of his money if a. he bets 1 dollar each time...
658 sym R (3353 sym/12 pcs)
DATA 605 Week 10 Discussion
Page 445 #28 Prove that P and (1/2)(I + P) have the same fixed vectors. Solution First we will show that \(\frac{1}{2}(I+P)x=x\) implies \(Px=x\). Expanding the formula: \(\frac{1}{2}(I+P)x \rightarrow \frac{1}{2}Ix + \frac{1}{2}Px =x\) As per the definition of the identity matrix, \(Ix=x\), so we can simplify to: \[ \frac{1}{2}x +\frac{1}{2} Px =...
1190 sym