Publications by Julia Ferris
Discussion Week 6
Page 90 Question 16 Prove that at least two people in Atlanta, Georgia have the same initials, assuming no one has more than four initials. #Number of people in Atlanta, Georgia num_in_atlanta = 496000 # Number of possible combinations of initials for 4 initials or less twoInitials = 26 * 26 threeInitials = 26 * 26 * 26 fourInitials = 26 * ...
584 sym
Homework 6 - DATA 605
Question 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? For green = 0, C(7, 5) For green = 1, C(7, 4) * C(5, 1) Total ways = C(7, 5) + (C(7, 4) * C(5, 1)) Answer: 196 ways library(pracma) ## Warning: package 'pracma' was buil...
4030 sym R (2236 sym/26 pcs)
Discussion Week 5
Page 71 Question 5 from Chapter 2.2 Continuous Density Functions Suppose you are watching a radioactive source that emits particles at a rate described by the exponential density f(t) = \(\lambda e^{-\lambda t}\), where λ = 1, so that the probability P(0, T) that a particle will appear in the next T seconds is P([0, T]) = \(\int_{0}^{T}{(\lam...
648 sym
Homework 5 - DATA 605
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 without the dise...
5584 sym R (2613 sym/73 pcs)
Homework 4 - DATA 605
In this first R chunk, the required libraries are loaded. Also, the file names are set. library(jpeg) library(magick) ## Warning: package 'magick' was built under R version 4.3.2 ## Linking to ImageMagick 6.9.12.98 ## Enabled features: cairo, freetype, fftw, ghostscript, heic, lcms, pango, raw, rsvg, webp ## Disabled features: fontconfig, x11 l...
1822 sym R (3278 sym/19 pcs) 4 img
Week 4 Response
a \(\begin{bmatrix} 2 \\ 1 \end{bmatrix}\) + b \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\) = \(\begin{bmatrix} 4 \\ 3 \end{bmatrix}\) \(\begin{bmatrix} 2 & 1 & 4 \\ 1 & 1 & 3 \end{bmatrix}\) Row reduce: library(pracma) ## Warning: package 'pracma' was built under R version 4.3.2 A <- matrix(c(2, 1, 4, 1, 1, 3), 2, 3, byrow = TRUE) rref(A) ## ...
656 sym R (206 sym/4 pcs)
Week 4 Discussion
Question M20 Page 403 The set B = {v1, v2, v3, v4} is a basis of the vector space P3, polynomials with degree 3 or less. Therefore ρB is a linear transformation, according to Theorem VRLT. Find a “formula” for ρB. In other words, find an expression for ρB(a + bx + cx^2 + dx^3). v1 = 1 - 5x - 22x^2 + 3x^3 v2 = -2 + 11x + 49x^2 - 8x^3 v...
3110 sym R (803 sym/8 pcs)
Homework 3 - DATA 605
Problem Set 1 Question 1: What is the rank of the matrix A? A = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix}\) Reduce to row echelon form: \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix}\) \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 &...
5439 sym
Discussion Week 3
Question: Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A. A = \(\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\) First, we need to find the characteristic polynomial of A. \(\begin{bmatrix} a - \lambda & b & c \\ d & e - \lambda & f \\ g ...
1609 sym
Homework 2 - 605
Problem Set 1 Question 1 Show proof that \(A^TA\) \(\neq\) \(AA^T\) in general. A = \(\begin{bmatrix} a & b &c \\ d & e & f \end{bmatrix}\) \(A^T\) = \(\begin{bmatrix} a & d \\ b & e \\ c & f \end{bmatrix}\) First, I will show \(A^TA\). \(\begin{bmatrix} a & d \\ b & e \\ c & f \end{bmatrix}\) * \(\begin{bmatrix} a & b &c \\ d & e & f \end{bma...
4002 sym R (19163 sym/23 pcs)