Publications by Group_Project: Venkata Naga Vamsidhar reddy karasani(vkara4), Anila Cheekati(vchee3), Venkata sai ram tirunagari(Vtiru5) , Pradeep kumar Naidu(Pnaid2), Simhadri Ramanjaneyulu(rsimh3), Subhalaxmi Rout(srout2)
Data 605 Assignment 2
Problem set 1 \((1)\) Show that \(A^T A ≠ A A^T\) in general. (Proof and demonstration.) Answer Method 1: Lets prove mathematically, \[\mathbf{A} = \left[\begin{array} {rrr} a & b \\ c & d \end{array}\right] \] Transpose of A \[\mathbf{A^T} = \left[\begin{array} {rrr} a & c \\ b & d \end{array}\right] \] \[\mathbf{A A^T} = \left[\begin{arr...
4419 sym R (1504 sym/22 pcs)
DATA 605 Assignment 8
\((11)\) 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? (See Exercise 10.) Answer \[E(X) = \mu/n = 1000/100 = 10 hours\] \(Z(14)\) Assume that X1 and X2 are independent random variables, each having an exponential density with parameter ...
1847 sym R (227 sym/8 pcs)
DATA 621 Assignment 2
Libraries library(dplyr) library(ggplot2) library(reshape2) library(kableExtra) library(DT) 1. Downloading the Data df <- read.csv("https://raw.githubusercontent.com/mkollontai/DATA621_GroupWork/master/HW2/classification-output-data.csv") df_hw2 <- df[,c('class', 'scored.class','scored.probability')] We have pulled the data and simplified our da...
4267 sym R (6105 sym/32 pcs) 4 img
Assignment 6
\((1)\) 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. Answer Given Red marbels = 54 White marbels = 9 Blue marbels = 75 Total marbels = 54 ...
8077 sym R (1074 sym/32 pcs) 2 img
DATA 605 Assignment 5
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. Solution: Create two random variables i.e B and C, by sampling 10,000 numbers between 0 and 1. library(ggplot2) set.se...
696 sym R (1656 sym/17 pcs) 7 img
DATA 605 - Assignment 4
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 X 2 matrix A \[A = \left[\begin{array} {rrr} 1 & 2 & 3 \\ -1 & 0 & 4 \\ \end{array}\right] \] write code in R to compute X = AAT and Y = ATA. Then, compute the eigenvalues and eigenvectors of X and Y using ...
2515 sym R (5168 sym/56 pcs)
SRout Assignment 3
Problem set 1 \((1)\) What is the rank of the matrix A? \[A = \left[\begin{array} {rrr} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{array}\right] \] Solution A <- matrix(c(1,2,3,4,-1,0,1,3,0,1,-2,1,5,4,-2,-3),nrow=4,byrow=TRUE) det(A) ## [1] -9 Matrix is invertible, so rank of the matrix is its dimentio...
3815 sym R (786 sym/14 pcs)
Dicussion 3
Exercise - T 10, page - 402 Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A. Solution: Let matrix \[A = \left[\begin{array} {rrr} -2 & 1 & -2 & -4 \\ 12 & 1 & 4 & 9 \\ 6 & 5 & -2 & -4 \\ 3 & -4 & 5 & 10 \end{array}\right] \] #install.packages("pracma...
458 sym R (465 sym/6 pcs)
Assignment 1
DATA621 HW1 Misha Kollontai, Matthew Baker, Erinda Budo, Subhalaxmi Rout, Don Padmaperuma 9/5/2020 Overview In this homework assignment, you will explore, analyze and model a data set containing approximately 2200 records. Each record represents a professional baseball team from the years 1871 to 2006 inclusive. Each record has the performance o...
11124 sym R (34360 sym/61 pcs) 23 img
DATA 605 Assignment 7
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 library(ggplot2) n <- 1000 k <- 20 Y <- c() for (i in 1:n){ Xn <- sample(1:k, 5, TRUE) Y <- c(Y, min(Xn)) } ggplot(data.frame(ta...
1473 sym R (2977 sym/33 pcs) 1 img