Publications by Abdelmalek Hajjam/ Monu Chacko
DATA 605 Discussion 14
Exercises 8.8 (6) \[f(x) = tan^{-1}(x); c = 0\] Key Idea: \[tan^{-1}(x) = \sum^\infty_{n = 0}(-1)^n\frac{x^{2n+1}}{2n+1}\] Derivatives for the first few n’s. Find the trend. \[\begin{align} f(x) &= tan^{-1}(x), &f(0) &= 0 \\ \\ f'(x) &= \frac{1}{x^2+1}, &f'(0) &= 1 \\ \\ f''(x) &= -\frac{2x}{(x^2+1)^2}, &f''(0) &= 0 \\ \\ f'''(x) &= -\fra...
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DATA 605 Discussion 13
Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? # Read data covid_ds <- read.csv(file = '...
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DATA 605 Assignment 11
Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) head(cars) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 7 4 ## 4 7 22 ## 5 8 16 ## 6 ...
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Data 605 -Discussion Week 12
Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? processors <- read.csv("full_data.csv") head(processors) ## date location new_cases new_deaths total_cases total_deaths ## 1 2019-12-31 Afghanistan 0 0 0 0 ...
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DATA 605 - Homework 10
Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if (a) he bets 1 dollar each time (timi...
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DATA 605 - Discussion 10
In American casinos, the roulette wheels have the integers between 1 and 36, together with 0 and 00. Half of the non-zero numbers are red, the other half are black, and 0 and 00 are green. A common bet in this game is to bet a dollar on red. If a red number comes up, the bettor gets her dollar back, and also gets another dollar. If a black or gre...
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DATA 605 Assignment 9
Q 11 (Page 363) The price of one share of stock in the Pilsdorff Beer Company is given by \(Y_n\) on the nth day of the year. Finn observes that the differences \(X_n = Y_{n+1} - Y_n\) appear to be independent random variables with a common distribution having mean \(\mu = 0\) and variance \(\sigma^2 = 1/4\). If \(Y_1 = 100\), estimate the probab...
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DATA 608 Final Project Proposal COVID-19
Final Project Proposal For this project I want to investigate the coronavirus data and find interesting insights from them Finding Dataset This is an emerging dataset and I intend to use dataset from https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases or https://ourworldindata.org/coronavirus-source-data . Total confirmed cases: h...
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LAW OF LARGE NUMBERS - DATA 605 Assignment 8
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? \[E[X_i] = \frac{1}{\lambda_i} = 1000\] Expected lifetime of a bulb is 1000 hours. \[\lambda_i = \frac{1}{1000}\] \(X_i\) is exponential so \[min\{X_1,X_2,...,X_{100}\} \sim exponential(\...
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Useful Videos
The Normal Distribution and the 68-95-99.7 Rule (5.2) Mode, Median, Mean, Range, and Standard Deviation (1.3) Chi Squared Test https://www.youtube.com/watch?v=qYOMO83Z1WU ...
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