Publications by yina qiao
DATA 605 HW5-YINA QIAO
Problem 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...
5357 sym Python (6984 sym/54 pcs)
DATA 605 W5D-YINA QIAO
Problem Statement 7 . A die is rolled until the first time T that a six turns up. (a) What is the probability distribution for T? (b) Find P(T > 3). (c) Find P(T > 6|T > 3) (a) What is the probability distribution for \(T\)? The probability distribution for \(T\), where \(T\) is the trial on which the first six appears, follows a geometric distrib...
462 sym
DATA 608 S2-yina qiao
Can the FED Control Inflation and Maintain Full Employment? Has the FED been able to fulfill the mandate given to it by Congress? Data Collection/Preprocessing library(httr) library(jsonlite) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects ar...
240 sym R (9692 sym/20 pcs) 3 img
DATA 605 HW4 YINA QIAO
Requirement: With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Provide full R code and discussion. File Loading and Preprocessing Provied data contains 17 images. # Define the file path where the images are located files <- list.files(path = "/Users/linda/Desktop/elearning/CUNY-MSDS/data 605/w4...
632 sym 2 img
W4D 605-YINA QIAO
C31† P349 For the linear transformation S compute the pre-images. \[ S: \mathbb{C}^3 \rightarrow \mathbb{C}^3, S (\begin{bmatrix}a\\b\\c\end{bmatrix}) = \begin{bmatrix}a - 2b -c \\3a-b+2c\\a+b+2c\end{bmatrix} \] \[ S^{-1}(\begin{bmatrix}-2\\5\\3\end{bmatrix}) \] \[ S^{-1}(\begin{bmatrix}-5\\5\\7\end{bmatrix}) \] Find rref for each vectors to see ...
1413 sym
DATA 605 W3 discussion-YINA QIAO
C24 Find the eigenvalues, eigenspaces, algebraic and geometric multiplicities for \[A = \begin{bmatrix} 1&−1&1\\ −1&1&−1\\ 1&−1&1 \end{bmatrix} \] A <- matrix(c(1, -1, 1, -1, 1, -1, 1, -1, 1), nrow = 3, byrow = TRUE) # Find the eigenvalues eigenvalues<-eigen(A)$value print(eigenvalues) ## [1] 3.000000e+00 8.881784e-16 0.000000e+00 # Find ei...
162 sym
DATA 605 C20
# Given matrix A matrixA <- matrix(c(18, -15, 33, -15, -4, 8, -6, 6, -9, 9, -16, 9, 5, -6, 9, -4), 4, 4) # Step 1: Find eigenvalues and eigenvectors eigen_result <- eigen(matrixA) # eigenvalues and eigenvectors eigenvalues <- eigen_result$values eigenvectors <- eigen_result$vectors # Check algebraic and geometric multiplicities for (i in 1:lengt...
5 sym
DATA 605 HW3-YINA QIAO
(1) What is the rank of the matrix A? A <- matrix(c(1,2,3,4, -1,0,1,3, 0,1,-2,1, 5,4,-2,-3), 4, byrow=T) qr(A)$rank ## [1] 4 (2) Given an mxn matrix where m > n, what can be the maximum rank? The minimum rank, assuming that the matrix is non-zero? Maximum Rank: For an \(m \times n\) matrix where \(m > n\...
4162 sym
DATA 605 HW2
Problem 1 1. Show that \(A^T A \neq AA^T\) in general. (Proof and demonstration.) Indirect Proof: Assume \(A^T A = AA^T\). If \(A = \begin{bmatrix} 1 & 3 \\ 2 & 5 \end{bmatrix}\) then \(A^T = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\). \(A^T A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix} \begin{bmatrix} 1 & 3 \\ 2 & 5 \end{bmatrix} = \begin{...
1589 sym
DATA 605 W2 discussion
C36 Find the rank and nullity of the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 & 1 & 1\\ 1 &3&2&0&4 \\ 1&2&1&1&1 \end{bmatrix} \] # Load necessary library library(pracma) A <- matrix(c(1, 2, 1, 1, 1, 1, 3, 2, 0, 4, 1, 2, 1, 1, 1), nrow = 3, byrow = TRUE) # Find the rank of A rank_A <- qr(A)$rank print(paste("Rank of A:",...
139 sym R (740 sym/6 pcs)