Publications by Enid Roman
Data_605_ERoman_HW7
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. The solution should be: For \[ 1 ≤ j ≤ k, m(j) = {{(k-j+1)^{n} - (k-j)^{n}} \over k^{n}} \] Since Y is the minimum value of Xi over all of...
2919 sym
Data_605_E.Roman_HW6
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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? # For the draw that contains 1 greenjelly beans we can have 5 choose 1 where 5 jelly beans can have 1 position choose(5,1) ## [1] 5 # For other spots must be filled with red jellyb...
3085 sym Python (5329 sym/54 pcs)
ERoman_Discussion6.rmd
Chapter 3 page 114 Use the program BinomialProbabilities to find the probability that, in 100 tosses of a fair coin, the number of heads that turns up lies between 35 and 65, between 40 and 60, and between 45 and 55. # Testing the outcome of heads or tails outcomes <- c("heads", "tails") sample(outcomes, size = 1, replace = TRUE) ## [1] "tail...
287 sym
Data_605_E.Roman_HW5
(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 the disease,...
4374 sym
ERoman_Discussion5.rmd
Page 12 Excercise 1 Modify the program CoinTosses to toss a coin n times and print out after every 100 tosses the proportion of heads minus 1/2. Do these numbers appear to approach 0 as n increases? Modify the program again to print out, every 100 times, both of the following quantities: the proportion of heads minus 1/2, and the number of head...
683 sym
E.Roman_Data_605_HW4 - Eigenshoe
Read Pix Set Up Initialization library(jpeg) ## Warning: package 'jpeg' was built under R version 4.2.2 library(OpenImageR) ## Warning: package 'OpenImageR' was built under R version 4.2.2 library(EBImage) ## ## Attaching package: 'EBImage' ## The following objects are masked from 'package:OpenImageR': ## ## readImage, writeImage getwd() #...
2089 sym R (13535 sym/50 pcs) 5 img
DATA 605 HOMEWORK WEEK 2
1. Problem set 1: (1) Show that ATA does not equal to AAT in general. (Proof and demonstration.) As per the text, A First Course of Linear Algebra, page 180, even if the sizes are right, matrix multiplication is not commutative — order matters. Please see proof in word document. Below I will demonstrate from the result that AT does not e...
1685 sym
DATA 605 - HOMEWORK WEEK 1 - IMAGE MANIPULATION
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(plotly) ## Warning: package 'plotly' was built under R version 4.2.2 ## Loading required package: ggp...
470 sym R (2485 sym/22 pcs) 5 img
Data 607 - Acquisition and Management - Assignment 1
In 2020 there was a high level of enthusiasm for voting in the general election. In the beginning of the year, voter registration had increased. Then COVID-19 pandemic hit and new registrations had suddenly decreased. As per the data taken registration numbers were even stronger in early 2020 than early 2016. Things changed dramatically in M...
5554 sym R (28033 sym/39 pcs) 5 img
Data 607 - Assignment # 2 - Movie_Rating with SQL
I chose six recent films and asked five different imaginary individuals to rate each of the movies they had seen from a scale of 1 to 5. Data Collection I created a database called movie_rating in a MySQL workbench to store the data in individual tables: Table 1: movie Table 2: name Table 3: review The SQL code for table creation: CREATE TABLE...
2875 sym R (8364 sym/25 pcs) 1 img