Publications by Jonathan Burns
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 ...
3143 sym R (1948 sym/11 pcs) 4 img
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...
844 sym
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...
1205 sym R (1490 sym/16 pcs) 1 img
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...
6 sym R (487 sym/2 pcs) 1 img
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 ...
1880 sym
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...
2897 sym
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 ...
1059 sym
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...
639 sym
Week 7 Discussion Ch.5 Question 17
Chapter 5 Question 17: The probability of a royal flush in a poker hand is p = 1/649,740. How large must n be to render the probability of having no royal flush in n hands smaller than 1/e? flush <- 1/649740 no_flush <- 1-flush prob <- qgeom(1/exp(1), prob = flush, lower.tail = F) ##Note that 1/e in this case is 1/exp(1) cat("n must be", prob...
199 sym
HW 6 JBurns
1. A bag contains 5 green and 7 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? choose(5,1)*choose(7,4)+choose(7,5) ## [1] 196 \(\text{Permutation: } P(n, r) = \frac{n!}{(n-r)!}\) \[ P(5, 1) = \frac{5!}{1!(5-1)!} = 5\] \[ P(7, 4) = \frac{7!}{4!(7-4)!} = 35...
4083 sym