Publications by Jie Zou
605: hw3
605: hw3 Jie Zou 2021-09-11 Problem set 1 What is the rank of the matrix A? \[\mathbf{A} = \begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -1 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix} \] A = matrix(c(1,2,3,4,-1,0,1,3,0,1,-2,1,5,4,-2,-3), 4,4, byrow = T) # the rank of square matrix will...
4713 sym R (217 sym/4 pcs)
605: Assignment6
605: Assignment6 Jie Zou 2021-10-02 note: W = ways, P = probability 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? let X = {number of green jellybeans being withdrawn} W(X < 2) = W(X = 0) + W(X = 1) wx0 = choose(7,5)*choose(5...
4047 sym R (2439 sym/41 pcs)
605: hw8
605: hw8 Jie Zou 2021-10-17 ex11 pg303 A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? The individual mean is: \(\lambda_i = \frac{1}{1000}\) while the company buys 100 lightbulbs, the accumulated mean is: \(\lambda = \sum \lambda_i = 100 ...
1738 sym R (256 sym/8 pcs)
605: discussion9
605: discussion9 Jie Zou 2021-10-20 ex3 pg338 A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. April just guesses on each question. A passing score is 30 or more correct answers. Compare the probability that June passes the exam with the probability that April passes it. the example is true-f...
909 sym R (476 sym/16 pcs)
605: discussion10
605: discussion Jie Zou 2021-10-30 ex6 pg422-423 In the Land of Oz example(Example 11.1), change the transition matrix by making R an obsorting state. This gives \[P = \begin{array} \s & R & N & S \\ R & 1 & 0 & 0 \\ N & 1/2 & 0 & 1/2 \\ S & 1/4 & 1/4 & 1/2 \end{array}\] Find the fundamental matrix N, and also Nc and NR. Interpret the results...
1415 sym
605: hw11
605: hw11 Jie Zou 2021-11-07 load data data(cars) explore data 50 observations in total, and there is no missing values. From speed histogram, it looks normally distributed, but from distance histogram, the plot is right skewed. From the scatter plot, speed and distance have positive linear relationship. # first few observations head(cars) ## ...
1329 sym R (1264 sym/14 pcs) 5 img
605： hw12
605: hw12 Jie Zou 2021-11-12 intro the data set contains the data from 2008. The variables include follow. Country: name of the country LifeExp: average life expectancy for the country in years InfantSurvival: proportion of those surviving to one year and more Under5Survival: proportion of those surviving to five or more TBFree: proportion of th...
5681 sym R (6287 sym/31 pcs) 3 img
605: hw13
605: hw13 Jie Zou 2021-11-20 1. Use integration by substitution to solv the integral below. \[\int 4e^{-7x} dx\] solution \[u = -7x \\ \int 4e^u dx\\ \frac{du}{dx} = -7 \\ dx = \frac{du}{-7} \\ \int 4e^u \frac{du}{-7} \\ =\frac{4}{-7} \int e^u du \\ =\frac{4}{-7} e^u \\ = \frac{4}{-7}e^{-7x} + C\] 2. Biologists are treating a pon...
3845 sym R (432 sym/2 pcs) 1 img
605: discussion14
605: discussion14 Jie Zou 2021-12-03 pg441 ex23-25 In the exercise, use the Limit Comparison test to determine the convergence of the given series; state what series is used for comparison. \[\sum_{n=1}^{\infty} \frac{1}{n^2-3n+5}\] Take the dominant term from denominator to form a comparison, I get \[\frac{1}{n^2}\] Perform Limit Comparison Te...
1792 sym
605: hw14
605: hw14 Jie Zou 2021-12-06 Taylor Series Expansions 1. \[f(x)=\frac{1}{1-x}\] calculate first 4 derivatives: \[f^{(1)}(x) = \frac{1}{(1-x)^2}\] \[f^{(2)}(x) = -\frac{2}{(x-1)^3}\] \[f^{(3)}(x) = \frac{6}{(x-1)^4}\] \[f^{(4)}(x) = -\frac{24}{(x-1)^5}\] plug these derivatives into Talor polynomial function, and set the \(c = 0\), it becomes \[\...
1826 sym