Publications by CHUNJIE NAN
DATA605_HW6_ChunjieNan
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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? These combinations are 0 green + 5 red, 1 green + 4 red choose(5,0)*choose(7,5) + choose(5,1)*choose(7,4) ## [1] 196 2. A certain congressional committee consists of 14 senators ...
4226 sym R (1218 sym/26 pcs)
DATA605_Week3_discussion
C12 library(Matrix) library(pracma) ## ## Attaching package: 'pracma' ## The following objects are masked from 'package:Matrix': ## ## expm, lu, tril, triu a <- matrix(c(1,2,1,0,1,0,1,0,2,1,1,0,3,1,0,1),nrow = 4, byrow=T) a ## [,1] [,2] [,3] [,4] ## [1,] 1 2 1 0 ## [2,] 1 0 1 0 ## [3,] 2 1 1 0 ## [4,...
77 sym R (398 sym/7 pcs)
DATA605_HW3_Chunjie_Nan
1. Problem set 1 1) What is the rank of the matrix A? \[A= \begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3\\ \end{bmatrix} \] The rank of the matrix refers to the number of linearly independent rows or columns in the matrix. ρ(A) is used to denote the rank of matrix A. Properties of the Rank of the Matrix:...
2548 sym R (1122 sym/30 pcs)
DATA605_HW4_ChunjieNan
With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Provide full R code and discussion. Import Libraries library(doParallel) ## Loading required package: foreach ## Loading required package: iterators ## Loading required package: parallel library(foreach) library(jpeg) library(OpenImageR) libra...
489 sym R (2818 sym/23 pcs) 3 img
DATA605_HW5_ChunjieNan
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 disease,...
6251 sym R (973 sym/52 pcs)
DATA605_HW8_ChunjieNan
11. A company buys 100 light bulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? According problem set 10, the exponential density has mean = \(\frac {\mu}{n}\), If \(X_{i}\) is an independent random variable, \(E[X_{i}] = \frac {1}{\lambda_{i}} = 1000\). Since, \(\fr...
1901 sym R (189 sym/8 pcs)
DATA608_Project_Proposal_ChunjieNan
Project Proposal Requirement This proposal must include: a link to the data source, an explanation of what you want to show, why this is relevant to a current policy, business, or justice issue, and which technologies you plan to use. Your instructor must approve this proposal: you may have to refine this somewhat. You will present your final pro...
4303 sym
DATA605_HW10_ChunjieNan
Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if he bets 1 dollar each time (timid st...
947 sym R (667 sym/4 pcs)
DATA605_HW15_ChunjieNan
1. Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. ( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 ) data<-data.frame(x=c(5.6,6.3,7,7.7,8.4),y=c(8.8,12.4,14.8,18.2,20.8)) reg<-lm(y~x,data) summary(reg) ## ## Call: ## lm(formula = y ~ x, data = data...
2627 sym R (677 sym/2 pcs)
DATA605_HW14_ChunjieNan
For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. 1. \(f(x) = \frac{1}{(1-x)}\) with generating derivatives, first derivative: \(f'(x) = \frac{1}{(1-x)^2}\) second derivative: \(f''(x) = \frac{2}{(1-x)^3}\) third derivative: \(f'''(x) = \frac{6}{(1-x)^4}\) fourth deriv...
1667 sym