Publications by Joey Bochnik
Week 14 Assignment
Week 14 Assignment This week, we’ll work out some Taylor Series expansions of popular functions. \(f (x) = 1/(1−x)\) \(f(x) = e^x\) \(f (x) = ln(1 + x)\) \(f(x)=x^{(1/2)}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assignment as an R- Markdo...
2953 sym
Discussion post week 14
Page 496 #31 In Exercises 31 – 32, approximate the value of the given def- inite integral by using the first 4 nonzero terms of the inte- grand’s Taylor series. 31.) \(\int^{\sqrt{\pi}}_{0} sin(x^2) dx\) The Taylor Series for sin(x) is given by : \(\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{(2n+1)!}\) Now substitute in \(x^2\) \(\sum_{n=0}^{\in...
878 sym
Week 13 Assignment
Problem 1 Use integration by substitution to solve the integral below \(\int_{}^{} 4e^{-7x} \, dx\) let \(u=-7x\) \(du=-7 dx\) \(dx=-\frac{1}{7}du\) Now substitute back into the integral: \(\int_{}^{} 4e^{u} * -\frac{1}{7} \, du\) \(-\frac{4}{7} \int_{}^{} e^{u} \, du=\) \(=-\frac{4}{7}e^u + c\) Substitute u = -7x \(=-\frac{4}{7}e^{-7x} + c\) Pro...
4118 sym Python (431 sym/6 pcs)
Week 13 Discussion
Page 179 Question 10 A boat is being pulled into a dock at a constant rate of 30ft/min by a winch located 10ft above the deck of the boat. At what rate is the boat approaching the dock when the boat is: 50 feet out? 15 feet out? 1 foot from the dock? What happens when the length of rope pulling in the boat is less than 10 feet long? Part A The pi...
1736 sym
Week 12 Assignment
Week 12 Assignment The attached who.csv dataset contains real-world data from 2008. The variables included follow. Country: name of the 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 TBFree: propor...
4927 sym R (5575 sym/33 pcs) 4 img
Document
library(Lahman) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union library(ggplot2) # Load team data teams_data <- Teams # Select only the relevant columns we will sel...
2297 sym R (30619 sym/23 pcs) 3 img
Week 11 Assignment
Week 11 Assignment Using the “cars” data set 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.) The cars data set is built into R and can be accessed easily through the variable “cars” library(d...
3743 sym R (2143 sym/19 pcs) 7 img
Week 11 Discussion
Discussion Week 11 Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? Introduction I will be using the built in Lahman data set in R to create the regression model. As a Baseball and Yankees fan the seemingly spike in strikeouts across the league (specifically...
3673 sym R (2703 sym/20 pcs) 5 img
Week 10 Assignment
Week 10 Homework Problem 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 he bets 1 dol...
3188 sym R (1590 sym/6 pcs)
Week 10 Discussion
Page 415 problem 15 Write a program to simulate the outcomes of a Markov chain after n steps, given the initial starting state and the transition matrix P as data (see Ex- ample 11.12). Keep this program for use in later problems. markov_chain <- function(initial_state, transition_matrix, n_steps) { current_state <- initial_state # Iterate thro...
759 sym Python (2990 sym/24 pcs)