Publications by Santiago Torres
605 Assignment 1
Assignment 1 S s_x=c(seq(-.5,.3,length.out=500),seq(-.3,.3,length.out=500),seq(-.3,.5,length.out=500)) s_y=c(seq(-.5,-1, length.out=225),rep(-1,50),seq(-1,-.3,length.out=225), seq(.3,-.3,length.out=500), seq(.3,1, length.out=225),rep(1,50),seq(1,.5,length.out=225)) s_z=rbind(s_x,s_y) plot(s_y~s_x, xlim=c(-1,1), ylim=c(-1,1)) T t_x=c(seq(-...
491 sym R (4898 sym/11 pcs) 10 img
RREF C.13
RREF.C13 solve the system of equations and convert to a matrix \(x_1 + 2x_2 + 8x_3 - 7x_4 = -2\) \(3x_1 + 2x_2 + 12x_3 - 5x_4 = 6\) \(-x_1 + x_2 + x_3 - 5x_4 = -10\) using the matlib package we can show each step as well: A <-matrix(c(1,3,-1,2,2,1,8,12,1,-7,-5,-5), nrow=3,ncol=4) b <- c(-2,6,10) echelon(A, b, verbose=TRUE, fractions=TRUE) ## ...
332 sym R (1872 sym/2 pcs)
D.C37
D.C37 Find the rank and nullity of the Matrix A \[ A = \left[ {\begin{array}{cc} 3 & 2 & 1 & 1 & 1\\ 2 & 3 & 0 & 1 & 1\\ -1 & 1 & 2 & 1 & 0\\ 1 & 1 & 0 & 1 & 1\\ 0 & 1 & 1 & 2 & -1\\ \end{array} } \right] \] using the Matrix and pracma package to solve this question: library(Matrix) ## ## Attaching package: 'Matrix' ## The following o...
341 sym R (601 sym/9 pcs)
Assignment 9
Assignment 9 p363: #11. The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by Yn on the nth day of the year. Finn observes that the differences Xn = Yn+1 − Yn appear to be independent random variables with a common distribution having mean µ = 0 and variance σ 2 = 1/4. If Y1 = 100, estimate the probab...
1318 sym R (220 sym/6 pcs)
Assignment 8
Assignment 8 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.) The expected value of the Exponential distribution is: λe^(-λx) n = 100 rate = 1000 n_rate = rate / n paste0("The first bulb will burn out at ", n_rate,...
883 sym R (443 sym/11 pcs)
STorres Assignment 6
Homework 6 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? We need to withdraw 5 jellybean total where only 1 or 0 of them are from the 5 green jellybeans: Choose 1 out of 5 green and then 4 out of 7 red plus 0 out of 5 green an...
4989 sym R (896 sym/12 pcs)
STORRES_Assignment3
Problem Set 1 What is the rank of the matrix A? \[ A = \left[ {\begin{array}{cc} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & 1\\ 5 & 4 & -2 & -3\\ \end{array}} \right] \] A <- matrix(c(1,-1,0,5,2,0,1,4,3,1,-2,-2,4,3,1,-3),nrow = 4,ncol=4) A ## [,1] [,2] [,3] [,4] ## [1,] 1 2 3 4 ## [2,] -1 0 1 3 ## [3,...
1038 sym R (1179 sym/23 pcs)
Assignment 4
Library library(here) ## here() starts at C:/Users/Santi/OneDrive/Documents/GitHub/DATA605/Assignments/HW4 library(jpeg) library(EBImage) library(OpenImageR) ## ## Attaching package: 'OpenImageR' ## The following objects are masked from 'package:EBImage': ## ## readImage, writeImage Load images here command returns the current directo...
782 sym R (3242 sym/15 pcs) 3 img
Storres Assignment5
Q1 (Bayesian). A new test for multinucleoside-resistant (MNR) human immunodeficiency virus type 1 (HIV-1) variants was recently developed. The test maintains 96% sensitivity, meaning that, for those with the disease, it will correctly report “positive” for 96% of them. The test is also 98% specific, meaning that, for those without the disease...
4326 sym R (2931 sym/50 pcs)
Assignment 7
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 . Using the proof explanation on Dartmouth we can find the distribution of Y in the following manner: X has k possibilities so we have \(k^n\) po...
2555 sym R (560 sym/4 pcs)