Publications by Arvind Sharma
Midterm_Solution
Question 1: Basic Data Analysis in R (Assignment+Discussion 1) In 1986, the Challenger space shuttle exploded during “throttle up” due to catastrophic failure of o-rings (seals) around the rocket booster. The data (real) on all space shuttle launches prior to the Challenger disaster are in the file challenger.csv. Load the data into R or Python...
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CPS_discussion
PROMPT The Current Population Survey (CPS) is a monthly survey of households conducted by the Bureau of Census for the Bureau of Labor Statistics. It provides a comprehensive body of data on the labor force, employment, unemployment, persons not in the labor force, hours of work, earnings, and other demographic and labor force characteristics. Expl...
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CLT
Central Limit Theorem Definition and Proof The Central Limit Theorem (CLT) is one of the most important theorems in statistics and data science. The CLT states that the sample mean (\(\bar{x}\)) of a probability distribution sample is a random variable with a mean value given by population mean \(\mu\) and standard deviation \(\sigma_{\bar{x}}\) (...
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CLT_LLN_relationship
The Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) are fundamental concepts in probability and statistics. 1 Law of Large Numbers (LLN): Definition: The Law of Large Numbers states that as the sample size increases (or as the number of trials in an experiment increases), the sample mean (or what) converges in probability to the pop...
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LLN
1 Introduction In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are perfor...
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HW5_template
Homework 5, Data Analysis Resources : Please have a look at re-emphasizing the core concepts of CLT, standard error, hypothesis testing, confidence interval and p-values. Please skim through them (~15 minutes) before attempting the assignment to refresh your memories. Please find the Open Intro Statistics textbook (OpenStat_textbook.pdf) in our Dr...
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Distributions_hypothesis_testing
0.1 Normal Distribution: 0.1.1 Definition: A normal distribution is a symmetric, bell-shaped probability distribution that is fully characterized by its mean (μ) and standard deviation (σ). In the context of student grades, a normal distribution suggests that a significant number of students perform close to the average grade, with fewer student...
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student_t_class_examples
Standard Error: In statistics, the standard error (SE) is a measure of how much the sample mean is expected to vary from the true population mean. It is a standard deviation of the sampling distribution of the sample mean. The standard error quantifies the precision of your sample mean estimate. The formula for standard error when estimating the po...
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ggplot2
Read this help file for R Markdown. 1 Set Up Clear all environments. Installing and loading all the libraries. Make sure you have the libraries installed. 2 Import Data Now, I will import my data. Make sure you comment out or exclude or do not use View(train) command. df <- read.csv("~/Library/CloudStorage/Dropbox/WCAS/Summer/Data Analysis/share/...
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Z_distribution
1 Z Scaling Z-scaling, also known as standardization or z-score normalization, is a common preprocessing step in statistics and machine learning. It involves transforming the features of a dataset so that they have a mean of 0 and a standard deviation of 1. The formula for z-scaling is: \[z=\dfrac{x-\mu}{\sigma}\] where: z is the standardized v...
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