Publications by Jie Zou
605: hw9
605: hw9 Jie Zou 2021-10-24 ex11 pg363 The price of one share of stock in the Pilsdorff Beer Company is given by \(Y_n\) on the n\(th\) day of the year. Finn observes that the differences \(X_n = Y_{n+1} -Y_n\) appear to be independent random variables with a common distribution having mean \(\mu = 0\) and variance \(\sigma^2 = 1/4\). If \(Y_1=1...
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605: discussion8
605:discussion Jie Zou 2021-10-15 ex.3 pg289 let \(X_1\) and \(X_2\) be independent random variables with common distribution \[px = (\begin{matrix} 0 & 1 & 2\\1/8&3/8&1/2 \end{matrix})\] find the distrubution of the sum \(X_1+X_2.\) let \(P_z = P(X_1 + X_2)\) px1_0 = px2_0 = 1/8 px1_1 = px2_1 = 3/8 px1_2 = px2_2 = 1/2 \(P_z(0) = P_{X_1}(0)*P_{X...
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605: assignment7
605: hw7 Jie Zou 2021-10-07 1. let X1, X2, …, Xn be n mutually independent random variables, each of which is uniformly distributed on the integers from 1 to k. Let Y denote the minimum of the Xi’s. Find the distribution of Y. each of which is uniformly distributed, which means that the probability of each X1, X2,….,Xn is a constant. they ...
1746 sym R (769 sym/25 pcs)
605: Assignment5
605: Assignment5 Jie Zou 2021-09-27 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 t...
5313 sym R (1798 sym/56 pcs)
605: assignment4
605: eigenshoes Jie Zou 2021-09-19 load libraries library(jpeg) library(EBImage) library(OpenImageR) ## ## Attaching package: 'OpenImageR' ## The following objects are masked from 'package:EBImage': ## ## readImage, writeImage get jpeg files # list file under directory files = list.files("./jpg", pattern = "\\.jpg") # the number of files...
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605: discussion4
605: discussion4 Jie Zou 2021-09-16 C25 pg. 443 Define the linear transformation \[T: C^3 ->C^2, T(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}) = \begin{bmatrix} 2x_1-x_2+5x_3 \\ -4x_1+2x_2 -10x_3 \end{bmatrix}\] Verify that \(T\) is a linear transformation. Solution \(1.proof: T(x+y) = T(x) + T(y)\) \[T(x+y) = \begin{bmatrix} 2(x_1+y_1)-(x...
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605: discussion3
discussion3 Jie Zou 2021-09-13 C24 pg. 387 Find the eigenvalues, eigenspaces, algebraic and geometric multiplities for \[\mathbf{A} = \begin{bmatrix} 1 & -1 & 1 \\ -1 & 1 & -1 \\ 1 & -1 & 1 \end{bmatrix} \] # the matrix A = matrix(c(1,-1,1,-1,1,-1,1,-1,1), nrow = 3, byrow = T) In order to compute \(\lambda\) value, we have \(det(A - \lambda I) =...
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605: w2_discusion
week2: discussion Jie Zou 2021-09-06 C25 – pg. 287 Show that the set W = \[\begin{Bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix}| & 3x_{1} - 5x_{2} = 12 \end{Bmatrix}\] from Example NSC2Z fails Property AC and Property SC. fail AC let x = \[\begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix}\] suppose that y\(\in\) W and y = \[\begin{bmatrix}...
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605： Assignment2
605: hw2 Jie Zou 2021-09-05 Problem 1 Show that \(A^{T}A \neq AA^{T}\) in general. (Proof and demostration) explore mxn matrix where \(m \neq n\) # 1. 2x3 matrix will have 3x2 transpose. The dimension of AA.T is 2x2, however, the dimension of A.TA is 3x3. Therefore, in general, a mxn matrix will have nxm transpose, the poduct of itself and it...
537 sym R (1776 sym/25 pcs)
605: discussion1
605: Discussion 1 Jie Zou 8/27/2021 C50 Question: A three-digit number has two properties. The tens-digit and the ones-digit add up to 5. If the number is written with the digits in the reverse order, and then subtracted from the original number, the result is 792. Use a system of equations to find all of the three-digit numbers with these prope...
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