Publications by Julia Ferris
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? # Height and weight data heightWeight <- read.csv("https://gist.githubusercontent.com/nstokoe/7d4717e96c21b8ad04ec91f361b000cb/raw/bf95a2e30fceb9f2ae990eac8379fc7d844a0196/weight-height.csv") 1. Visualize t...
4088 sym R (1641 sym/10 pcs) 5 img
Homework 11 - DATA 605
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.) Linear Model: stopping_distance = 3.932(speed) - 17.579 In this linear model, we see the y-intercept is -17.579, and t...
4125 sym 5 img
Discussion Week 10
Chapter 11 Page 467 Question 7 A rat runs through the maze shown in Figure 11.7. At each step it leaves the room it is in by choosing at random one of the doors out of the room. knitr::include_graphics("/Users/TEMP/Downloads/screenshot.jpg") Figure 11.7: Maze for exercise 7. (a) Give the transition matrix P for this Markov chain. Answer: See ...
3001 sym R (1135 sym/6 pcs) 1 img
Homework 10
Smith is in jail and has 1 dollar; he can get out on bail if he has $8. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability 0.4 and loses A dollars with probability 0.6. Find the probability that he wins 8 dollars before losing all of his money if. . . (a) he bets 1 dollar each time (ti...
843 sym R (1350 sym/10 pcs)
Homework 9 - DATA 605
Question 1 The price of one share of stock in the Pilsdorff Beer Company is given by \(Y_n\) on the nth 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 \(\mu\) = 0 and variance \(\sigma ^2\) = 1/4. If \(Y_1\) = 100, estimate the...
4627 sym R (569 sym/12 pcs)
Discussion Week 9
Chapter 10 Exercise 3 Page 392 In the chain letter problem (see Example 10.14) find your expected profit if \(p_0\) = 1/2, \(p_1\) = 0, and \(p_2\) = 1/2. \(p_0\) = 1/6, \(p_1\) = 1/2, and \(p_2\) = 1/3. Also, show that if \(p_0\) > 1/2, you cannot expect to make a profit. Chain letter problem from Example 10.14: The chain required a participa...
2104 sym
Discussion Week 8
If X is normally distributed, with mean \(\mu\) and variance \(\sigma^2\) , find an upper bound for the following probabilities, using Chebyshev’s Inequality: a) \(P(|X - \mu| \geq \sigma)\) b) \(P(|X - \mu| \geq 2 \sigma)\) c) \(P(|X - \mu| \geq 3 \sigma)\) d) \(P(|X - \mu| \geq 4 \sigma)\) Chebyshev’s Inequality = \(P(|X - \mu| \ge...
1530 sym
Homework 7
Question 1: Page 303 Problem 11 A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? mean = lifetime / n Answer: 10 hours mean = 1000 / 100 print(mean) ## [1] 10 Question 2: Page 303 Problem 14 Assume that X1 and X2 are independent random var...
1920 sym
Discussion Week 7
Question 6, Page 279 Let T be a random variable with range [0,\(\infty\)] and fT its density function. Find \(\mu\)(T) and \(\sigma^2\)(T) if both conditions are met: 1 – When t < 0, fT(t) = 0 2 – When t > 0, fT(t) = \(3e^{-3t}\) \(9te^{-3t}\) \(3/(1 + t)^4\) To find \(\mu\)(T), you will find E(X), which is equal to the following: \(\int_{...
705 sym
Homework 7 - DATA 605
Let X1, X2, . . . , Xn be n mutually independent random variables, each of which is uniformly distributed on the integers from 1 to k. Let Y denote the minimum of the Xi’s. Find the distribution of Y . Y is the minimum of X. Let x be the smallest number. The probability that Y is greater than or equal to x is multiplying the probability of e...
2357 sym