Publications by Abdelmalek Hajjam/ Monu Chacko
DATA 605 Discussion 8 - LAW OF LARGE NUMBERS
Page 312 1: A fair coin is tossed 100 times. The expected number of heads is 50, and the standard deviation for the number of heads is (100 · 1/2 · 1/2)1/2 = 5. What does Chebyshev’s Inequality tell you about the probability that the number of heads that turn up deviates from the expected number 50 by three or more standard deviations (i.e., ...
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Data 605 HW 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. If \(K^n\) is the sum of variables then \((k-1)^n\) would represent varaibles where \(X_i\) does not contain 1 \[P(X=1)=\frac { { k }^{ n }-{ ...
1560 sym R (1125 sym/30 pcs)
DATA 621 Home Work 2 - Confusion Matrix
require("plyr") require("knitr") require("psych") require("knitr") require("ggplot2") require("pracma") require("caret") require("pROC") 1. Download the classification output data set(attached in Blackboard to the assignment). df <- read.csv(url('https://raw.githubusercontent.com/monuchacko/cuny_msds/master/data_621/Homework2/classificati...
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DATA 605 Discussion
HW Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Note that the point (B,C) is then chosen at random in the unit square. Find the probability that B <- runif(10000, min=0, max=1) C <- runif(10000, min=0, max=1) B + C < 1/2 sum ((B+C) < 0.5) / length(B) ## [1] 0.1245 BC < 1/2 sum ((B*C) < 0.5...
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Assignment 6 DATA 605
HW 6 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_b <- 54 + 75 all <- 54 + 9 + 75 round(r_b/all, 4) ## [1] 0.9348 You are going to play ...
3958 sym R (1837 sym/28 pcs)
DATA 605 Discussion 6
Exercise 3: How many seven-element subsets are there in a set of nine elements? if n is total element (here 9) and k is the subset element (here 7) the we can say it is \(\left( \begin{array}{cccc} n \\ k\end{array}\right)\) (n choose k) There is n way we can choose the first element and n-1 ways we can choose the second and n-2 ways we can choos...
534 sym R (89 sym/4 pcs)
Data 621 HW 1
Purpose This report covers an attempt to build a model to predict number of wins of a baseball team in a season based on several offensive and deffensive statistics. Resulting model explained about 36% of variability in the target variable and included most of the provided explanatory variables. Some potentially helpful variables were not include...
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Probability Discussion 5
Exercises 22 (Introduction to Probability) Assume that we are making raisin cookies. We put a box of 600 raisins into our dough mix, mix up the dough, then make from the dough 500 cookies. We then ask for the probability that a randomly chosen cookie will have 0, 1, 2, . . . raisins. Consider the cookies as trials in an experiment, and let X be ...
1153 sym R (65 sym/2 pcs)
Singular Value Decomposition (SVD)
library(Matrix) library(matrixcalc) ASSIGNMENT 4 1.Problem set 1 In this problem, we’ll verify using R that SVD and Eigenvalues are related as workedout 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 \(X = AA^T\) and \(Y = AT^A\). Then, compute the eigen values...
1853 sym R (4058 sym/47 pcs) 1 img
FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS
library(matrixcalc) library(pracma) ASSIGNMENT 3 1.Problem set 1 What is the rank of the matrix A? \[ A= \left[ \begin{array}{cccc} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{array} \right] \] A <- matrix(c(1, 2, 3, 4,-1, 0, 1, 3, 0, 1, -2, 1, 5, 4, -2, -3), nrow=4, byrow = TRUE) A ## ...
2484 sym R (891 sym/19 pcs)