Publications by David Blumenstiel
Data 606 Lab 7
North Carolina births In 2004, the state of North Carolina released a large data set containing information on births recorded in this state. This data set is useful to researchers studying the relation between habits and practices of expectant mothers and the birth of their children. We will work with a random sample of observations from this da...
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Data 606 Homework 7
Working backwards, Part II. (5.24, p. 203) A 90% confidence interval for a population mean is (65, 77). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 25 observations. Calculate the sample mean, the margin of error, and the sampl...
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Data 606 Blumenstiel Project Proposal
Data Preparation #Loading the dataframe df <- read.csv('https://raw.githubusercontent.com/davidblumenstiel/data/master/kaglemovies/tmdb_5000_movies.csv') #Trimming out the parts variables we aren't interested in movies <- df[,c(1,9,13,14,19)] #Taking out observations which have a budget under 1000 (gets rid of some suspect observations) mo...
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Data 605 Homework 2
Problem Set 1 1: Show that A transoposed * A does not equal A * A transposed At = A transposed Let's use A = [1,2] as an example [3,4] This means that At = [1,3] [2,4] Now lets try At * A: [1,3] * [1,2] = [10,14] [2,4] [3,4] [14,20] And now A * At: [1,2] * [1,3] = [5 ,11]...
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Data 605 Homework 7
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 We have n integers from 1 to k, and Y is going to be the lowest one. I think what this is asking for is the number of ways we can get the lowes...
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Data 605 Homework 6
1: A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. The probability of getting a red or blue marble is the number of red + blue marbles, over the t...
7822 sym R (1685 sym/18 pcs)
Data 605 Homework 3
Problem Set 1 What is the rank of the matrix A? A <- matrix(c(1,-2,0,5,2,0,1,4,3,1,-2,-2,4,3,1,-3), ncol=4) A ## [,1] [,2] [,3] [,4] ## [1,] 1 2 3 4 ## [2,] -2 0 1 3 ## [3,] 0 1 -2 1 ## [4,] 5 4 -2 -3 Rank is how many rows and columns are not comprised of other rows and columns. We can find t...
3535 sym R (1989 sym/25 pcs)
Data 605 Homework 4
Problem Set 1 Given matrix A A <- matrix(c(1,-1,2,0,3,4),nrow = 2) A ## [,1] [,2] [,3] ## [1,] 1 2 3 ## [2,] -1 0 4 write code in R to compute X = A AT and Y = AT A. AT <- t(A) # sets AT to the transpose of A AT ## [,1] [,2] ## [1,] 1 -1 ## [2,] 2 0 ## [3,] 3 4 X <- A %*% AT #Multiplies the m...
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Data 605 Assignment 5
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. So, broken down from the text, we can interperet that B and C are always going to be between 0 and 1 (interval), and have the same probability of being any number within that range (uniform den...
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Data 605 Assignment 8
Assignment 8 David Blumenstiel 10/12/2020 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.) To recap Exercise 10: of n independent random variables, the minimum value (M) of the independent random variables is going to...
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