Publications by Mahmud Hasan Al Raji
Data605_Assignment08
Exercise-11: 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) Ans-11: From exercise 10, the minimum value has mean = \(\mu\)/\(n\) Here, \(\mu\) \(=\) \(1000\) \(and\) \(n\) \(=\) \(100\) Therefore, the expected time fo...
2155 sym
Data605_Assignment07
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 . ** Ans-1: Let, y be a value in the range between 1 and k. As Y is the minimum of the Xi’s, then the probability distribution of Y will be...
2351 sym
Data605_Assignment06
Question-1: A bag contains 5 green and 7 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? Ans-1: # way_1 = C(7,5) # withdrawal of 5 red jellybeans from 7 red jellybeans # way_2 = C(7,4)*C(5,1) # withdrawal of 4 red jellybeans from 7 red jellybeans and withdr...
4417 sym Python (3651 sym/24 pcs)
Data605_Assignment05
Question-1: (Bayesian). A new test for multinucleoside-resistant (MNR) human immunodeficiency virus type 1 (HIV-1) variants was recently developed. The test maintains 96% sensitivity, meaning that, for those with the disease, it will correctly report “positive” for 96% of them. The test is also 98% specific, meaning that, for those without ...
11466 sym Python (7877 sym/80 pcs)
data605_assignment04
This assignment is done to build and visualize eigenimagery that accounts for 80% of the variability of the given image data set. To do so, following steps are being followed: Uploading the image files as a list that containing the image features i.e. names,pixels etc. Converting the multi-dimensional data list into an array Transforming the a...
2079 sym R (1360 sym/13 pcs) 3 img
Data605_Assignment03
Problem Set1: 1.What is the rank of the matrix \(A\) = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \\ \end{bmatrix}\) Ans-1: Performing row transformations to make the matrix into echelon form: \(R_2 = R_2 + R_1,\) \(A\) = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 7 \\ 0 & 1 & -2 & 1 \\ 5...
6610 sym R (715 sym/14 pcs)
Assignment02_data605
Problem Set 1 (1) Show that \(A^TA\) \(\neq\) \(AA^T\) in general. (Proof and demonstration) Ans-1: Proof: Let, A is a matrix of order m x n (where m \(\neq\) n), then its transpose matrix \(A^T\) will be the order of n x m. So, the multiplication of the two matrices \(A^T\) and \(A\) i.e.the product matrix, \(A^TA\) will be the order of n x ...
3035 sym
data605_hw1
Building the first letters for both first and last name using point plots: First letters for the first name is “M” and the last name is “A” The following code will build MA: x <- c(rep(-1,500), seq(-0.25,-1,length.out=500), seq(-0.25,0.5,length.out=500), rep(0.5,500), seq(1.25,2,length.out=500), ...
1118 sym 5 img
Lab:1 Intro to R and RStudio
Introducttion: The main purpose of the ‘Assignment:Lab1’ is to analyse a specific data set named, ‘present’, to understand and determine different information that are hidden in that data set.The data set refers to the present day birth records in the United States.Different data exploration and data visualization techniques will be u...
3958 sym R (4443 sym/23 pcs) 1 img
Assignment_01_data607
Required libraries library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union library(htmltab) library(stringr) 1:Identification of majors that contain either “DATA...
1490 sym R (2549 sym/16 pcs)