Publications by Arvind Sharma
t_distribution
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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CLT_discussion_solution
Central Limit Theorem I. Definition and Proof In class, we saw that 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 deviati...
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RDD
1. Introduction Without a random process that separates the treatment and control group, the treatment effect can be identified if the assignment to the treatment group follows a regression discontinuity design (RDD). This requires a (running) variable which, at a certain threshold, separates the observations into a treatment and control group. 2....
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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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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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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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hts
Please read up on the source code. gts example Data These are infant mortality counts. This data set is an example of gts, where the total infant mortality count in Australia can be first disaggregated by sex then by state, or vice versa. library(hts) ## Loading required package: forecast ## Registered S3 method overwritten by 'quantmod': ## met...
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HW3
rm(list = ls()) # Clear environment gc() # Clear unused memory ## used (Mb) gc trigger (Mb) limit (Mb) max used (Mb) ## Ncells 526290 28.2 1169047 62.5 NA 669277 35.8 ## Vcells 974784 7.5 8388608 64.0 32768 1840474 14.1 cat("\f") # Clear the console dev.off # Clear the charts ## fun...
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Diff_in_Diff_Discussion
rm(list = ls()) # Clear environment gc() # Clear unused memory ## used (Mb) gc trigger (Mb) limit (Mb) max used (Mb) ## Ncells 525460 28.1 1166668 62.4 NA 669291 35.8 ## Vcells 966463 7.4 8388608 64.0 32768 1840372 14.1 cat("\f") # Clear the console graphics.off() # Clear the charts libra...
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Discussion3_data_types_versus_structures
In R, classes represent the type or category of data, and the basic classes include numeric, integer, character, logical, and complex. class() Data Structure are some ways to organize and store the data. Common data structures in R include vectors, matrices, arrays, lists, data frames, and factors. typeof() 1 Classes in R: Classes in R refer to th...
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