Publications by Forhad Akbar
DATA605- Homework 09
DATA 605: Homework 09 Forhad Akbar 03/28/2020 Load Packages library(knitr) 11 page 363 The price pf one share of stock in the Pilsdorff Beer Company is given by Yn on the nth day of the year. Finn observes that the differences Xn = Yn+1 - Yn appear to be independent random variables with a common distribution having mean u=0 and variance sigma s...
3821 sym R (279 sym/7 pcs)
DATA605- Homework 08
DATA 605: Homework 08 Forhad Akbar 03/19/2020 Load Packages library(knitr) 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.) \[ u=1000\\ n=100\\ E[x]=\frac{u}{n}=\frac{1000}{100}=10 \] Assume that X1 and X2 are inde...
3469 sym R (14 sym/1 pcs)
DATA605- Assignment 08 (Discussion)
Assignment 08 (Discussion): Chapters 8 Forhad Akbar 03/17/2020 Load Packages library(knitr) Problem Statement Chapter 8, Page 323, Exercise 16 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 ...
1882 sym R (868 sym/6 pcs) 4 img
DATA605- Homework 07
DATA 605: Homework 07 Forhad Akbar 03/12/2020 Load Packages library(knitr) 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 . Solution: By the definition of the CFD, we can derive the followin...
2741 sym R (683 sym/31 pcs)
DATA605- Assignment 07 (Discussion)
Assignment 07 (Discussion): Chapters 6 Forhad Akbar 03/10/2020 Load Packages library(knitr) Problem Statement Chapter 6, Page 250, problem 21 Let X be a random variable which is Poisson distributed with parameter λ. Show that E(X) = λ We are given the following hint: \[ e^{x}=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+.... \] Proof Our hint is ...
1798 sym R (14 sym/1 pcs)
DATA605- Homework 05
DATA 605: Homework 05 Forhad Akbar 02/28/2020 Load Packages library(knitr) Problem set 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. Proof: # generate random numbers...
885 sym R (2534 sym/21 pcs)
DATA605- Homework 04
DATA 605: Homework 04 Forhad Akbar 02/20/2020 Load Packages library(knitr) library(pracma) 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 x 2 matrix A \(A\quad =\quad \begin{bmatrix} 1 & 2 & 3 \\ -1 & 0 & 4 \end{bmatrix}\) write code in R to compute...
2173 sym R (2637 sym/20 pcs) 4 tbl
DATA605- Assignment 04 (Discussion)
Assignment 04 (Discussion): Chapters LT & R Forhad Akbar 02/19/2020 Load Packages library(knitr) Problem Statement The problem C25, selected page 443, Define the linear transformation \(T\quad :\quad { C }^{ 3 }\rightarrow { C }^{ 2 },\quad T(\begin{bmatrix} { x }_{ 1 } \\ { x }_{ 2 } \\ { x }_{ 3 } \end{bmatrix})\quad =\quad \begin{bmatrix} {...
1354 sym R (14 sym/1 pcs)
DATA605- Homework 03
DATA 605: Homework 03 Forhad Akbar 02/12/2020 Load Packages library(knitr) library(pracma) 1. Problem set 1 What is the rank of the matrix A? \(A\quad =\quad \begin{vmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{vmatrix}\) The set of pivot columns of any reduced row echelon form matrix is known as Rank. Tr...
5868 sym R (833 sym/15 pcs)
DATA605- Homework 02
DATA 605: Homework 02 Forhad Akbar 02/07/2020 Load Packages library(knitr) library(geometry) 1. Problem set 1 Show that \({ A }^{ T }A\neq A{ A }^{ T }\) in general. (Proof and demonstration.) Let \(A=\begin{vmatrix} a & b \\ c & d \end{vmatrix}\quad { A }^{ T }=\begin{vmatrix} a & c \\ b & d \end{vmatrix}\) \(A{ A }^{ T }=\begin{vmatrix} a ...
3590 sym R (2094 sym/38 pcs)