Publications by Shovan Biswas

Central Limit Theorem

30.12.2020

Central Limit Theorem Central Limit Theorem Load Packages Problem Statement Shovan Biswas 2020/03/23 Load Packages library(knitr) Problem Statement Problem 1 selected from page 352 of “Introduction to Probability”, by Charles M. Grinstead and J. Laurie Snell. A die is rolled 24 times. Use the Central Limit Theorem to estimate the proba...

1070 sym R (455 sym/15 pcs)

Sums of Independent Rand Variables

30.12.2020

Sums of Independent Rand Variables Sums of Independent Rand Variables Load Packages Problem Set 1 Shovan Biswas 2020/03/16 Load Packages library(knitr) library(matlib) Problem Set 1 The answers are in the following pages. Marker: 605-08 ...

232 sym R (31 sym/1 pcs) 2 img

Mix Regression Double Integral

30.12.2020

Mix Regression Double Integral Mix Regression Double Integral LOad Packages Question 1: Question 2: Question 3: Question 4: Question 5: Shovan Biswas 2020/05/11 LOad Packages library(ggplot2) library(tidyverse) library(knitr) library(data.table) Question 1: Find the equation of the regression line for the given points. Round any final v...

2922 sym R (724 sym/7 pcs) 3 img

Rank EigenValues EigenVectors

29.12.2020

Rank EigenValues EigenVectors Rank EigenValues EigenVectors Load Packages Problem Set 1 Problem Set 2 Shovan Biswas 2020/02/10 Load Packages library(knitr) Problem Set 1 What is the rank of the matrix A? Answer: I’ll first code the matrix A, in the following code chunk. A <- matrix(c(1, -1, 0, 5, 2, 0, 1, 4, 3, 1, -2, -2, 4, 3, 1, -3),...

3583 sym R (759 sym/11 pcs) 3 img

Eigenvalues

29.12.2020

Eigenvalues Eigenvalues Load Packages Problem Statement Shovan Biswas 2020/02/12 Load Packages library(knitr) Problem Statement The problem T20, selected from page 333 of “A First Course in Linear Algebra”, by Robert A. Bleezer. T20 (page 333): Suppose A is a square matrix. Prove that a single vector may not be an eigenvector of A for ...

391 sym R (14 sym/1 pcs) 1 img

Matrix Inverses and Systems of Linear Equations

29.12.2020

Matrix Inverses and Systems of Linear Equations Matrix Inverses and Systems of Linear Equations Problem Statement Load Packages Shovan Biswas 2020/01/28 Problem Statement The problem T25, selected from page 216 of “A First Course in Linear Algebra”, by Robert A. Bleezer. T25 The notation A^k means a repeated matrix product between k cop...

1980 sym R (110 sym/2 pcs)

Discrete and Continuous Probability Distributions

29.12.2020

Discrete and Continuous Probability Distributions Discrete and Continuous Probability Distributions Load Packages Problem Statement Shovan Biswas 2020/02/26 Load Packages library(knitr) Problem Statement The problem 17 and 19 selected from page 37 of “Introduction to Probability”, by Charles M. Grinstead and J. Laurie Snell. The answer...

396 sym R (14 sym/1 pcs) 3 img

Linear Transformation and Representations

29.12.2020

Linear Transformation and Representations Linear Transformation and Representations Load Packages Problem Statement Shovan Biswas 2020/02/18 Load Packages library(knitr) Problem Statement The problem C24, selected from page 478 of “A First Course in Linear Algebra”, by Robert A. Bleezer. The proof is in the following pages. Marker: 60...

355 sym R (14 sym/1 pcs) 3 img

Basic Vector Operations and R Program to Solve Linear Equations

29.12.2020

Basic Vector Operations and R Program to Solve Linear Equations Basic Vector Operations and R Program to Solve Linear Equations Problem Set 1 Load Packages Problem Set 2 Shovan Biswas 2020/01/30 Problem Set 1 You can think of vectors representing many dimensions of related information. For instance, Netix might store all the ratings a user ...

3507 sym R (2946 sym/25 pcs)

Computational Math and Matrix Factorization

29.12.2020

Computational Math and Matrix Factorization Computational Math and Matrix Factorization Problem Set 1 Load Packages Problem Set 2 Shovan Biswas 2020/02/06 Problem Set 1 Show that A^T A≠AA^T in general. (Proof and demonstration.) For a special type of square matrix A, we get A^T A=AA^T. Under what conditions could this be true? (Hint: The...

2104 sym R (3495 sym/21 pcs) 1 img