Publications by Rajwant Mishra, Priya Shaji, Debabrata Kabiraj, Isabel Ramesar, Sin Ying Wong and Fan Xu
DATA 605 02[46835] : Week 8 Discussion
P-Introduction to Probability Chapter 8. Law of Large Numbers 8.2 Law of Large Numbers for Continuous Random Variables Exercise 16 Page 323 Let \(Z = X/Y\) where \(X\) and \(Y\) have normal densities with mean \(0\) and standard deviation \(1\). Then it can be shown that \(Z\) has a Cauchy density. Write a program to illustrate this result b...
1903 sym R (854 sym/5 pcs) 4 img
DATA 605 02[46835] : Week 7 Discussion
P-Introduction to Probability Chapter 5. Important Distributions and Densities 5.2 Important Densities Exercise 16 Page 221 Let \(X\) be a random variable with density function \(f_X(x)=\begin{cases} cx(1-x), &if\ 0 < x < 1,\\0, &otherwise.\end{cases}\) What is the value of \(c\)? What is the cumulative distribution function \(F_X\) for \(X\...
962 sym R (938 sym/2 pcs) 2 img
DATA 605 02[46835] : HomeWork Assignment 7
ASSIGNMENT 7 Question 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 . Answer k <- 30 Y <- list() i <- 1 for(i in 1:100) { x <- sample(k, 1, replace = TRUE) Y[length(Y) + 1] <- lis...
4953 sym R (4393 sym/37 pcs) 4 img
DATA 605 02[46835] : HomeWork Assignment 5
ASSIGNMENT 5 Question Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions. Note that the point (B,C) is then chosen at random in the unit square. Find the probability that Answer Creating two random variables, B and C, by sampling 100,000 number...
1082 sym R (3525 sym/17 pcs) 7 img
DATA 605 02[46835] : Week 5 Discussion
P-Introduction to Probability CHAPTER 2. CONTINUOUS PROBABILITY DENSITIES 2.2. CONTINUOUS DENSITY FUNCTIONS Exercise 22 Page 84 Write a program to carry out the following experiment. A coin is tossed 100 times and the number of heads that turn up is recorded. This experiment is then repeated 1000 times. Have your program plot a bar graph for ...
784 sym R (557 sym/2 pcs) 1 img
DATA 605 02[46835] : HomeWork Assignment 4
ASSIGNMENT 4 IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - 2014 1. Problem set 1 In this problem, we’ll verify using R that SVD and Eigenvalues are related as worked out in the weekly module. Given a 3 2 matrix A \[ A = \left[\begin{array}{rrr}1 & 2 & 3\\-1 & 0 & 4\end{array}\right] \] Write code in R to compute \[X = AA^T\\and\\Y = A^TA...
3025 sym R (5809 sym/75 pcs) 4 tbl
DATA 605 02[46835] : Week 4 Discussion
L-A First Course in Linear Algebra Chapter LT: Linear Transformations Section LT Subsection NLTFO Page 444 C43 Define: \[ T:p_3 \rightarrow p_2\\by\\ T(ax+bx+cx^{2}+dx^{3})=b+2cx+3dx^{2} \] Find the pre-image of 0. Does this linear transformation seem familiar? Find the pre-image of 0 Lets understand what the pre-image is http://mathworl...
1360 sym
DATA 605 02[46835] : HomeWork Assignment 3
ASSIGNMENT 3 IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - 2014 1. Problem set 1 (1) What is the rank of the matrix A? \[ A = \left[\begin{array}{rrr}1 & 2 & 3 & 4\\-1 & 0 & 1 & 3\\0 & 1 & -2 & 1\\5 & 4 & -2 & -3\end{array}\right] \] (a) Solution using R A = matrix(c(1,2,3,4, -1,0,1,3, 0,1,-2,1, 5,4,-2,-3), nrow=4, ncol=4, byrow=TRUE) pa...
8259 sym R (2621 sym/44 pcs)
DATA 605 02[46835] : Week 3 Discussion
L-A First Course in Linear Algebra Chapter E: Eigenvalues Section EE Subsection ECEE Page 388 C24 C24 Find the eigenvalues, eigenspaces, algebraic and geometric multiplicities for \[\mathbf{A} = \left[\begin{array}{rrr}1 & -1 & 1\\-1 & 1 & -1\\1 & -1 & 1\end{array}\right] \] A <- matrix(c(1,-1,1, -1,1,-1, 1,-1,1), nrow=3, ncol=3, byrow=TRUE)...
650 sym R (2005 sym/34 pcs)
DATA 605 02[46835] : Week 2 Discussion
L-A First Course in Linear Algebra Chapter D: Determinants Section DM Page 353 C24 Doing the computations by hand, find the determinant of the matrix below. \[\mathbf{A} = \left[\begin{array}{rrr}-2 & 3 & -2\\-4 & -2 & 1\\2 & 4 & 2\end{array}\right] \] (a) Solution using R A = matrix(c(-2,-4,2,3,-2,4,-2,1,2), nrow=3, ncol=3, byrow=FALSE) A ...
1785 sym R (177 sym/4 pcs)