Publications by Tora Mullings
605 - Discussion week 6
K and A: 1 way each. Hyphen (-): 1 way. l1 and l2 (letters): \(26 \times 26\) ways. n1, n2, and n3 (numbers): \(10 \times 10 \times 10\) ways. Total Number of License Plate Numbers The total number of ways is the product of the choices for each component: \[ \text{Total Ways} = 1 \times 1 \times 26 \times 26 \times 10 \times 10 \times 10 \] tot...
355 sym
HW 5 - 605
1. prevalence_rate <- 0.001 sensitivity <- 0.96 specificity <- 0.98 total_population <- 100000 cost_per_case <- 100000 test_cost <- 1000 positive_given_disease <- sensitivity positive_given_no_disease <- 1 - specificity disease_given_positive <- (positive_given_disease * prevalence_rate) / ((positive_given_disease * prevalence_rate) + (pos...
99 sym
DATA 605 - Discussion Week 5
Suppose you choose at random a real number \(X\) from the interval \([2, 10]\). Find the density function \(f(x)\) and the probability of an event \(E\) for this experiment, where \(E\) is a subinterval \([a, b]\) of \([2, 10]\). Density Function \(f(x)\) \[ f(x) = \frac{1}{b - a} \] \(a = 2\) and \(b = 10\), so: \[ f(x) = \frac{1}{10 - 2} \] De...
861 sym
605 - HW4
This code was mostly taken from the eigenshoes document here: https://rpubs.com/R-Minator/eigenshoes library(imager) # resize function library(jpeg) # readJPEG num=20 files=list.files("jpg",pattern="\\.jpg")[1:num] height=1200; width=2500;scale=20 plot_jpeg = function(path, add=FALSE) { jpg = readJPEG(path, native=T) # read the file r...
117 sym R (2119 sym/13 pcs)
605 - Discussion week 4
Suppose \(U\) and \(V\) are vector spaces, and let \(Z : U \rightarrow V\) be defined by \(Z(u) = 0_V\) for every \(u \in U\). We want to prove that \(Z\) is a (stupid) linear transformation. For any \(u_1, u_2 \in U\), we have \[ Z(u_1 + u_2) = 0_V \] \[ Z(u_1) + Z(u_2) = 0_V + 0_V = 0_V \] \(Z(u_1 + u_2) = Z(u_1) + Z(u_2)\) For any \(u \in U\...
521 sym
605 - HW3
Question 1: Find the rank of the matrix. library(pracma) library(cmna) ## ## Attaching package: 'cmna' ## The following objects are masked from 'package:pracma': ## ## cubicspline, horner, newton, nthroot, romberg, secant, wilkinson library(Matrix) ## ## Attaching package: 'Matrix' ## The following objects are masked from 'package:pracm...
2381 sym R (1215 sym/14 pcs)
605_Discussion_week3
Matrix \(D\): \[ D = \begin{bmatrix} -2 & 1 & -2 & -4 \\ 12 & 1 & 4 & 9 \\ 6 & 5 & -2 & -4 \\ 3 & -4 & 5 & 10 \end{bmatrix} \] Solve the characteristic equation \(\text{det}(D - \lambda I) = 0\), where \(\lambda\) is the eigenvalue and \(I\) is the identity matrix. The equation is: \[ \text{det}(D - \lambda I) = \text{det}\left(\begin{bmatrix} ...
2140 sym
HW 2 - 605
\[\begin{equation} Prove AA^{T} \neq A^{T}A \end{equation}\] \[\begin{equation} Let A=\begin{bmatrix} w & y \\ x & z \end{bmatrix} \end{equation}\] \[\begin{equation} Then, A^{T}=\begin{bmatrix} w & x \\ y & z \end{bmatrix} \end{equation}\] \[\begin{equation} AA^{T} = \begin{bmatrix} ww + yy & xw + yz \\ xw + yz & xx + xz \end{bmatrix} \e...
791 sym
hw1 - 605
library(animation) x=c(rep(0,500),seq(0,1,length.out=1000), rep(1,500)) y=c(seq(-1,1,length.out=500),rep(0,1000), seq(-1,1,length.out=500)) z=rbind(x,y) plot(y~x, xlim=c(-3,3), ylim=c(-3,3)) dev.control('enable') myani=ani.record(reset=TRUE, replay.cur=FALSE) a=diag(2) x11() for (i in seq(-3,3,length.out=100)) { a[1,1]=i newmat=ap...
6 sym R (1162 sym/2 pcs) 1 img
DATA 624: HW 10
library(tidyverse) library(arules) library(arulesViz) library(cluster) library(factoextra) df <- read.transactions("GroceryDataSet.csv", header=FALSE, sep=",") summary(df) ## transactions as itemMatrix in sparse format with ## 9835 rows (elements/itemsets/transactions) and ## 169 columns (items) and a density of 0.02609146 ## ## most f...
12 sym R (5172 sym/8 pcs) 1 img