Publications by Jonathan Burns
Week 7 Discussion Ch.5 Question 17
Chapter 5 Question 17: The probability of a royal flush in a poker hand is p = 1/649,740. How large must n be to render the probability of having no royal flush in n hands smaller than 1/e? flush <- 1/649740 no_flush <- 1-flush prob <- qgeom(1/exp(1), prob = flush, lower.tail = F) ##Note that 1/e in this case is 1/exp(1) cat("n must be", prob...
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HW 6 JBurns
1. 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? choose(5,1)*choose(7,4)+choose(7,5) ## [1] 196 \(\text{Permutation: } P(n, r) = \frac{n!}{(n-r)!}\) \[ P(5, 1) = \frac{5!}{1!(5-1)!} = 5\] \[ P(7, 4) = \frac{7!}{4!(7-4)!} = 35...
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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...
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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_...
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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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