Publications by Jonathan Burns
HW6 Discussion WK6 Ch.3 Q10
In a ten-question true-false exam, and the probability that a student gets a grade of 70 percent or better by guessing. Answer the same question if the test has 30 questions, and if the test has 50 questions. 10 Questions pbinom(7, size = 10, prob = 0.5, lower.tail = F) ## [1] 0.0546875 30 Questions pbinom(21, size = 30, prob = 0.5, lower.tail...
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Discussion Ch.2 Exercise 1 JBurns
library(ggplot2) In the spinner problem (see Example 2.1) divide the unit circumference into three arcs of length 1/2, 1/3, and 1/6. Write a program to simulate the spinner experiment 1000 times and print out what fraction of the outcomes fall in each of the three arcs. Now plot a bar graph whose bars have width 1/2, 1/3, and 1/6, and areas eq...
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Discussion Week 5 response
R Markdown This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com. When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within...
482 sym Python (3478 sym/11 pcs) 2 img
JBurns_HW5
#Question 1 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 those witho...
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Week 4 Discussion C40 JBurns
C40: If T: \(\mathbb{C}^{2}\) \(\rightarrow\) \(\mathbb{C}^{2}\) satisfies T \(\left (\begin{bmatrix} 2 \\1 \end{bmatrix} \right)\) = \(\begin{bmatrix} 3 \\4 \end{bmatrix}\) and T \(\left (\begin{bmatrix} 1 \\1 \end{bmatrix}\right )\) = \(\begin{bmatrix} -1 \\2 \end{bmatrix}\) find T \(\begin{bmatrix} 4 \\3 \end{bmatrix}\) Because \(\begin{bma...
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Week 4 HW JBurns 605
#Task ##With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Provide full R code and discussion #Packages used library(doParallel) ## Warning: package 'doParallel' was built under R version 4.3.2 ## Loading required package: foreach ## Warning: package 'foreach' was built under R version 4.3.2 ##...
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Homework 3 JBurns
library(pracma) ## Warning: package 'pracma' was built under R version 4.3.2 What is the rank of the matrix A? I will show my method for Reduced Row Echelon Form and then double check my solution using the pracma Rank() function. \[ A = \begin{bmatrix} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & 1\\ 5 & 4 & -2 & -3 \end{bmatrix} \] \(R_...
3756 sym R (1064 sym/20 pcs)
Q22 Discussion 3
Question C22 - Without using a calculator, find the eigenvalues of the matrix \(B\). \[ B = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix} \] Solve to get the characteristic equation for the eigenvalues: \(B\) is the original matrix and \(\lambda I\) is \(\lambda\) * \(\textbf{The Identity Matrix}\) \[ \text{det}(B - \lambda I) = 0 \] The m...
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C12 p.64 Week 1 Discussion - JBurns
C12 Solve the given vector equation for a, or explain why no solution exists: \[\begin{equation} \text{a} \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix} + 4 \begin{bmatrix} 3 \\ 4 \\ 2 \end{bmatrix} = \begin{bmatrix} -1 \\ 0 \\ 4 \end{bmatrix} \end{equation}\] Step 1: Apply a and 4 to the vectors: \[\begin{equation}...
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C26 p.278 JBurns Discussion Week 2
library(pracma) ## Warning: package 'pracma' was built under R version 4.3.2 #C26. p.278: Doing the computations by hand, find the determinant of the matrix A. A <- matrix(c(2,0,3,2,5,1,2,4,3,0,1,2,5,3,2,1), nrow = 4, byrow = T) A ## [,1] [,2] [,3] [,4] ## [1,] 2 0 3 2 ## [2,] 5 1 2 4 ## [3,] 3 0 1 2 #...
483 sym R (336 sym/6 pcs)