Publications by Jonathan Burns
HW Week 12 JBurns
Import WHO csv file <- "C:\\Users\\jashb\\OneDrive\\Documents\\Masters Data Science\\Spring 2024\\Fundamentals of Computational Mathematics DATA 605\\Week 12\\who.csv" who <- read.csv(file) 1. Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, s...
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WK11 Discussion JBurns
Kaggle Link: https://www.kaggle.com/datasets/sakshisatre/the-boston-housing-dataset file = "C:\\Users\\Jonathan Burns\\OneDrive\\Documents\\Masters Data Science\\Spring 2024\\DATA 605\\Boston (1).csv" df <- read.csv(file) There were a bunch more variables but I picked the 5 I thought would be the most impactful. model <- lm(MEDV ~ CRIM + AGE + DI...
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WK11 HW JBurns
library(tidyverse) 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.) head(cars) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 7 4 ## 4 7 ...
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WK10 Question 8. JBurns
Question 8: 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 pr...
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WK10 HW JBurns
R Markdown library(markovchain) library(diagram) 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 o...
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Week 10 response
library(markovchain) library(diagram) weatherStates <- c("Rain", "Nice", "Snow") byRow <- TRUE weatherMatrix <- matrix(data = c(0.5, 0.25, 0.25, 0.5, 0.0, 0.5, 0.25, 0.25, 0.5), byrow = byRow, nrow = 3, dimnames = list(weatherStates, weatherStates)) m...
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HW 9 JBurns
1 11 page:363 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 $ = 0$ and variance \(\sigma^2 = \frac{1}{4}\). If \(Y_1 ...
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HW8 JBurns
11 and #14 on page 303 of probability text #1 on page 320-321 Question 11. A company buys 100 light bulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? (See Exercise 10.) According to question 10, we can surmise that in an exponential situation, the minimum value wi...
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Discussion Week 8 JBurns
Question 11: The Pilsdorff beer company runs a fleet of trucks along the 100 mile road from Hangtown to Dry Gulch, and maintains a garage halfway in between. Each of the trucks is apt to break down at a point X miles from Hangtown, where X is a random variable uniformly distributed over [0, 100]. For reference: Chebyshev’s Inequality: \(P(|X ...
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Week 7 Assignment JBurns
Question 1 Hi Dr. Larry, I really struggled with this quesiton and look forward to the walk through in class, see you then! Solution: Since Y is the minimum of the \(Xi\) and each \(Xi\) is uniformly distributed from 1 to \(k\), then each possibility for \(Xi\) is represented by \(k^n\). Question 2 Part A: The question states that there is o...
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