Publications by Samuel I Kigamba
DATA 605 Assignment 7
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. \[For 1≤j≤k, m(j)= \frac{(k-j+1)^n-(k-j)^n}{k^n}\] Your organization owns a copier (future lawyers, etc.) or MRI (future doctors). This mac...
1952 sym R (404 sym/22 pcs)
DATA 605 Assignment6
HW6 A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. R = 54 W = 9 B = 75 n = R + W + B #p(R or B) = p(R) + p(B) p_R_or_B = R/n + B/n ro...
4221 sym R (2591 sym/33 pcs) 1 tbl
DATA 605 Discussion 6
A more refined inequality for approximating n! is given by \[\sqrt{2\pi n}(\frac{n}{2})^ne^{1/(12n+1)} < n! < \sqrt{2\pi n}(\frac{n}{2})^ne^{1/(12n)}\] Write a computer program to illustrate this inequality for n = 1 to 9. n_factoral <- function(n) { # Perform a check for n = 1 to 9. if (1 <= n & n <= 9) { n_check = TRUE } else ret...
333 sym R (1527 sym/17 pcs)
DATA 605 Assignment5
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: B + C < 1/2. \[P(B+C<1/2)\] \[=P(X+Y<1/2)\] \[=P(0<X<1/2,0<Y<1/2−x)\] \[=∫^{1/2}_0∫^{1/...
1123 sym R (107 sym/2 pcs)
DATA 605 Assignment4
#ASSIGNMENT 4 IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - 2014 1. Problem Set 1 In this problem, well verify using R that SVD and Eigenvalues are related as worked out in the weekly module. Given a 3 × 2 matrix A \[A =\begin{Bmatrix} 1 & 2 & 3\\ −1 & 0 & 4\\ \end{Bmatrix}\] Write code in R to compute X = AAT and Y = ATA A = matrix(...
2936 sym R (2532 sym/27 pcs)
DATA 605 Assignment3
ASSIGNMENT 3 IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - 2014 #install.packages('pracma') library(pracma) library(matlib) 1 Problem set 1 (1) What is the rank of the matrix A? Note: Rank is equal to the number of non-zero rows in the reduced row echelon form (RREF). \[A=\begin{Bmatrix} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & ...
2919 sym R (1644 sym/15 pcs) 3 img
DATA 605 Discussion 2
page 352, Chapter D, 3. Compute the determinant of the matrix \[ \begin{pmatrix} 3 & 9 & -2 & 4 & 2\\ 0 & 1 & 4 & -2 & 7\\ 0 & 0 & -2 & 5 & 2\\ 0 & 0 & 0 & -1 & 6\\ 0 & 0 & 0 & 0 & 4\\ \end{pmatrix} \] By hand determinant computation Using R’s det() function to confirm the by hand computation. x = matrix(c(3,9,-2,4,2, 0,1...
309 sym R (153 sym/2 pcs) 1 img
DATA 605 Assignment1
ASSIGNMENT 1 IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - FALL 2014 1. Problem set 1 You can think of vectors representing many dimensions of related information. For instance, Netflix might store all the ratings a user gives to movies in a vector. This is clearly a vector of very large dimensions (in the millions) and very sparse as the us...
3245 sym R (2216 sym/18 pcs)
DATA 605 Discussion 1
#install.packages('matlib') library(matlib) ## Warning: package 'matlib' was built under R version 3.6.2 Instructions: Pick one of the exercises in the readings this week. Solve the exercise as best as you can. If you have issues, explicate them, so that all of us can help. My selection: A First Course in Linear Algebra page 42. For problems C...
837 sym R (10230 sym/6 pcs)
DATA 607 Final Project
SECTION ONE - INTRODUCTION Objective of this analysis. Goal: My objective in this project is seeking to understand the relationship between population growth and the crime rates in the United States between the year 1994 to 2018 and to comment and conclude on the overal pattern. Data sources. To analyze the crime rates in the US for the period ...
4710 sym R (11927 sym/22 pcs)