Publications by Johnny Rodriguez
Discussion Week 14
Taylor Series Expansion for \(f(x) = \sin(2x + 3)\) Chapter 8.8, #27 Function and Its Derivatives: First derivative \(f'(x) = 2\cos(2x + 3)\) Second derivative \(f''(x) = -4\sin(2x + 3)\) Third derivative \(f'''(x) = -8\cos(2x + 3)\) Fourth derivative \(f''''(x) = 16\sin(2x + 3)\) Evaluate at \(x = 0\): \(f(0) = \sin(3)\) \(f'(0) = 2\cos(3)\) \...
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Data 605 Discussion 13
A 24 ft ladder is leaning against a house while the base is pulled away at a constant rate of 1 ft/s. (Page 179, #9 ) At what rate is the top of the ladder sliding down the side of the house when the base is: (a) 1 foot from the house? (b) 10 feet from the house? (c) 23 feet from the house? (d) 24 feet from the house? We apply the concept of relat...
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Data 605 Homework Week 13
Q1 Use integration by substitution to solve the integral below. \[ \int 4e^{-7x} \, dx \] Identify the substitution Let: \[ u = -7x \] Compute \(du\): \[ du = -7dx \] and dx: \[ dx = -\frac{1}{7}du \] Rewrite the integral using \(u\) Substitute \(u\) and \(dx\): \[ \int 4e^u \cdot -\frac{1}{7}du \] This simplifies to: \[ -\frac{4}{7} \int e^u \, ...
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Data 605 Homework Week 12
Load Libraries and Read File data <- read.csv("https://raw.githubusercontent.com/johnnydrodriguez/data605/main/who.csv", header = TRUE, sep = ',', na.strings="", fill = TRUE) head(data) ## Country LifeExp InfantSurvival Under5Survival TBFree PropMD ## 1 Afghanistan 42 0.835 0.743 0.99769 0.00022884...
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Discussion Week 12
Student Performance Dataset (from Kaggle) Source: https://www.kaggle.com/datasets/nikhil7280/student-performance-multiple-linear-regression?resource=download Description: The Student Performance Dataset is a dataset designed to examine the factors influencing academic student performance. The dataset consists of 10,000 student records, with each re...
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Discussion Week 11
2018 Central Park NYC Squirrel Census Does the temperature have a relationship to the number of squirrel? The hypothesis is that as the temperature increases so will the numnber of squirrel sightings in NYC Central Park. library(dplyr) library(tidyr) library(readr) library(stringr) squirrels <- read.csv("https://raw.githubusercontent.com/johnnydro...
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Data 605 Homework Week 11
Linear model for stopping distance as a function of speed For the exercise, I performed the linear regression analysis on the orginal data as well the data that was tranformed using box-cox and logarithm methods. plot(cars$speed, cars$dist, main="Scatter plot of Stopping Distance vs Speed", xlab="Speed", ylab="Stopping Distance") Simple Linear Reg...
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Data 605 HW Week 10
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 dollar each time (ti...
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Discussion Week 10
A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability p that the digit that enters this stage will be changed when it leaves and a probability q = 1 − p that it won’t. Form a Markov chain to represent the process of trans...
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Data 605 Discussion Week 9
CLT Page 354 #3 A piece of rope is made up of 100 strands. Assume that the breaking strength of the rope is the sum of the breaking strengths of the individual strands. Assume further that this sum may be considered to be the sum of an independent trials process with 100 experiments each having expected value of 10 pounds and standard deviation 1. ...
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