Publications by Esteban Aramayo
DATA605 - Homework 08
SUMS OF CONTINUOUS RANDOM VARIABLES Exercise 11 (Page 303) 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? (See Exercise 10.) Exercise 10: Let \(X_1, X_2, . . . , X_n\) be n independent random variables each of which has an exponential den...
9209 sym R (152 sym/4 pcs)
DATA605 - Homework 09
CONTINUOUS INDEPENDENT TRIALS Exercise 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 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...
7452 sym R (318 sym/3 pcs)
DATA605 - Homework 10
Markov Chains / Random Walks 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...
8274 sym R (962 sym/7 pcs) 1 img
DATA605 - Final Exam - Problem 2 of 3
library(tidyverse) library(keras) library(nnet) library(caret) Final Exam Final Problem 2. 40 points. 2.1 Go to Kaggle.com and build an account if you do not already have one. It is free. 2.2 Go to https://www.kaggle.com/c/digit-recognizer/overview, accept the rules of the competition, and download the data. You will not be required to sub...
14168 sym R (5337 sym/25 pcs) 33 img
DATA605 - Final Exam - Problem 1 of 3
library(igraph) # used to compute the Page Rank of the n square matrix A Final Exam Final Problem 1. 30 Points PAGERANK: AN APPLICATION OF PROBABILITY AND LINEAR ALGEBRA 1. Playing with PageRank You’ll verify for yourself that PageRank works by performing calculations on a small universe of web pages. Let’s use the 6 page universe that w...
12634 sym R (5309 sym/27 pcs) 2 img
DATA605 - Final Exam - Problem 3 of 3
library(dplyr) library(tidyr) library(ggplot2) library(naniar) library(randomForest) library(purrr) Final Exam Final Problem 3. 30 points. You are to compete in the House Prices: Advanced Regression Techniques competition https://www.kaggle.com/c/house-prices-advanced-regression-techniques . I want you to do the following. 3.1 Descriptive...
27825 sym R (23190 sym/65 pcs) 2 img
DATA605 - Homework 15
Week 15, Functions of Several Variables: 9-15 May Exercise 1. Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. \[( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 )\] ### Solution Define the points mypoints <- data.frame('x'=c(5.6, 6.3, 7, 7.7, 8.4), ...
16790 sym R (1055 sym/25 pcs)
DATA605 - Homework 14
Week 14, Taylor Series Approximations: 2-8 May This week, we’ll work out some Taylor Series expansions of popular functions. \(f(x) = \frac {1}{(1−x)}\) \(f(x) = e^x\) \(f(x) = ln(1 + x)\) \(f(x) = x^{1/2}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please s...
10078 sym
DATA605 - Homework 13
Week 13, Univariate & Multivariate Calculus: 23 Apr - 1 May Exercise 1 Use integration by substitution to solve the integral below. \(\int4e^{-7x}dx\) Solution \(\int4e^{-7x}dx\) Define a new variable u as follows: \(u = -7x => du = -7dx => dx = -\frac{1}{7}du\) Now replace original integral in terms of \(u\) variable: \(\int -\frac{4}{7}e^{u}d...
16818 sym R (781 sym/15 pcs) 3 img
DATA605 - Homework 11
library(ggplot2) library(dplyr) Week 11, Regression Analysis in R 1: 4-10 Apr 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.) SOLUTION: Explore the Data Be...
11718 sym R (2334 sym/13 pcs) 3 img