Publications by Dirk Hartog
Homework wk5
library(stats) Question 1 (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 tho...
7582 sym R (2041 sym/48 pcs)
Discussion board 5
Exercise 11 page 36 What odds should a person give in favor of the following events? A card chosen at random from a 52 card deck is an ace Two Heads will turn up when a coin is tossed twice Boxcars (2 6’s) will turn up when two dice are rolled Since we can find the probability of each event \(p(E)\) when can use \(p/(1 -p)\) to find \(r/s\) or ...
765 sym
Homework wk4
Set up library(doParallel) ## Loading required package: foreach ## Loading required package: iterators ## Loading required package: parallel library(foreach) library(jpeg) library(EBImage) # list.files looks at the folder given in path directory and creates a list of all file names. files=list.files(path='/Users/dirkhartog/Desktop/CUNY_MSDS/DATA_6...
345 sym R (4767 sym/25 pcs) 3 img
Homework wk3
Problem set 1 1. What is the rank of matrix A? \(\begin{bmatrix} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & 1\\ 5 & 4 & -2 & -3 \end{bmatrix}\) First we want to put the matrix into its reduced row echelon form to see how many pivot columns or non - zero rows we have. Steps to get RREF Arref <- A Arref[2,] = Arref[2,] + Arref[1,] Arref[4,] = Ar...
4619 sym
Discussion board 4
Exercise C16 Pg. 349 Find the Matrix representation of \(T : C^3 \rightarrow C^4 , T\) \[\begin{bmatrix} x\\ y\\ z \end{bmatrix}\] = \[\begin{bmatrix} 3x + 2y +z\\ x+y+z\\ x-3y\\ 2x+3y+z \end{bmatrix}\] ) Using Theorom MLTCV - Matrix Linear Transformation, Column Vectors we can find the matrix representation \(C_1 = T(e_1) =\) [ \[\begin{bmatrix} ...
1079 sym
Homework wk3
Problem set 1 1. What is the rank of matrix A? \(\begin{bmatrix} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & 1\\ 5 & 4 & -2 & -3 \end{bmatrix}\) First we want to put the matrix into its reduced row echelon form to see how many pivot columns or non - zero rows we have. Steps to get RREF Arref <- A Arref[2,] = Arref[2,] + Arref[1,] Arref[4,] = Ar...
4615 sym
Discussion board 3
Exercise C20 Pg. 306 Find the eigenvalues, eigenspace, algebreic mulitplicities and geometric multiplicities for the matrix below \[\begin{bmatrix} -12 & 30\\ -5 & 13 \end{bmatrix}\] 1. Finding the eighenvalues and algebraic multiplicities \((-12 - \lambda)(13 - \lambda) - (30 * 5)\) \(-156 - 13\lambda + 12\lambda +\) \(\lambda^2\) \((\lambda-3)(...
747 sym
Homework wk2
Problem Set 1 Show that \(A^TA \neq AA^T\) in general. (Proof and demonstration). If we have a 2 x 3 matrix A: \[\begin{bmatrix} -1 & -3 & 0\\ 2 & 2 & 3 \end{bmatrix}\] And a 3 x 2 matrix \(A^T\) \[\begin{bmatrix} -1 & 2\\ -3 & 2\\ 0 & 3 \end{bmatrix}\] \(A^TA\) will result in a 3 x 3 matrix and \(AA^T\) will result in a 2 x 2 matrix based on the...
1228 sym
Homework wk1
library(gifski) Build the first letters for both your first and last name using point plots in R x <- c(rep(-2,500),seq(-2,-1, length.out = 1000),rep(-1,250),seq(-1,-2, length.out = 1000), rep(0,500),seq(0,1,length.out=1000), rep(1,500)) y <- c(seq(-1,1,length.out=500), seq(1,0.5,length.out=1000), seq(0.5,-0.5,length.out=250),seq(-0.5,-1,l...
438 sym R (1635 sym/6 pcs) 1 img
Discussion board 2
Exercise C24, page 278 Doing the computations by hand, find the determinant of the matrix below A <- matrix(c(-2,3,-2,-4,-2,1,2,4,2), nrow = 3, byrow = T) A ## [,1] [,2] [,3] ## [1,] -2 3 -2 ## [2,] -4 -2 1 ## [3,] 2 4 2 Using the row expansion technique A[1,1] * ((A[2,2] * A[3,3]) - (A[3,2] * A[2,3])) - A[1,2] * ((A[...
171 sym