Publications by Ashish Kumar
Data605-Week3-Discussion
data-605-week3-Discussion Ashish Kumar 02/10/2020 Chapter E, Exercise EE.C22 Without using a calculator, find the eigenvalues of the matrix B. \[ B = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix} \] Solution To find the eigenvalues of A, we must solve det(λI-B) =0 for λ.Where I is Identitity Matrix. \[ det(λ\begin{bmatrix} 1 & 0 \\ 0 & 1 \en...
1048 sym
Akumar-Assignment2
data-605-week2-Assignment Ashish Kumar 02/08/2020 Problem set 1 Show that ATA ≠ AAT in general. (Proof and demonstration.) You can use R-markdown to submit your responses to this problem set. If you decide to do it in paper, then please either scan it or take a picture using a smartphone and attach that picture. Please make sure that the pict...
1843 sym R (2284 sym/25 pcs)
Data605-Week2-Discussion
data-605-week2-Discussion Ashish Kumar 02/04/2020 Chapter D, Section DM, Question M11 Find a value of k so that the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 0 & 1 \\ 2 & 3 & k \end{bmatrix} \] has \[det(A) = 0 \] or explain why it is not possible. Solution \[|A| = 1\begin{bmatrix} 0 & 1 \\ 3 & k \end{bmatrix} -2 \begin{bmatrix} 2 & 1 \\ 2 ...
576 sym R (124 sym/2 pcs)
Data605-Week1
data-605-week1-Assignment Ashish Kumar 01/30/2020 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 user might have rated only ...
2934 sym R (1055 sym/13 pcs)
data-605-week4-Discussion
data-605-week4-Discussion Ashish Kumar 02/17/2020 Chapter LT, Exercise LT.C20 Let \[ w = \begin{bmatrix} -3 \\ 1 \\ 4 \end{bmatrix} \] compute S(w) two different ways. First use the definition of S, then compute the matrix-vector product \[C_w\] Suppose \[S:C_3→C_4\] is defined by \[S(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}) = \begin{b...
886 sym R (346 sym/6 pcs)
data-605-week7-Assignment
data-605-week7-Assignment Ashish Kumar 03/12/2020 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 . n <- 100000 # Lets consider sample size of 100000 j <- 100 size <- 100 Y <- c() for (i in...
1321 sym R (1802 sym/25 pcs) 1 img
data-605-week10-Discussion
data-605-week10-Discussion Ashish Kumar 04/01/2020 CHAPTER 11. MARKOV CHAINS Exercise 8 Page 414 A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability p that the digit that enters this stage will be changed when it leaves...
1049 sym
data-605-week11-Assignment
data-605-week11-Assignment Ashish Kumar 04/14/2020 Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) head(cars) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 ...
1545 sym R (1526 sym/11 pcs) 3 img
data-605-week13-Discussion
data-605-week13-Discussion Ashish Kumar 04/20/2020 Batter up The exercise is a part of datacamp course located here:- https://bookdown.org/markhoff/css/machine-learning-week-1-linear-and-multiple-regression.html The movie Moneyball focuses on the “quest for the secret of success in baseball”. It follows a low-budget team, the Oakland Athleti...
5462 sym R (1560 sym/15 pcs) 7 img
data-605-week14-Assignment
data-605-week14-Assignment Ashish Kumar 04/28/2020 1. Use integration by substitution to solve the integral below. \(\color{red} {\int 4e^{-7x}dx}\) Let \(u = -7x\) or \(\cfrac { du }{ dx } = -7\Rrightarrow\) \({ dx } = \cfrac { -1 du}{ 7 }\) Hence, \({\int 4e^{-7x}dx}\) \(\Rrightarrow\cfrac {-4}{7}{\int e^{u}du}\) Now solving: \({\int e^{u}du}\...
3782 sym R (543 sym/9 pcs) 2 img