Publications by Santiago Torres
Assignment 10
Assignment 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 he bets 1 dollar each ...
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PageRank First create the A matrix that represents our 6 page internet and introduce decay with a B matrix - 5 points: A_matrix <- matrix(c(0,1/6,1/3,0,0,0, 1/2,1/6,1/3,0,0,0, 1/2,1/6,0,0,0,0, 0,1/6,0,0,1/2,1, 0,1/6,1/3,1/2,0,0, 0,1/6,0,1/2,1/2,0 ),nrow = 6...
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Assignment 15 Santiago Torres 5/15/2022 Assignment 15 Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. ( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 ) x <- c(5.6,6.3,7,7.7,8.4) y <- c(8.8,12.4,14.8,18.2,20.8) regression <- lm(y~x) summary(r...
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Assignment 14 This week, we’ll work out some Taylor Series expansions of popular functions. • \(f(x) = \frac{1}{(1-x)}\) • \(f(x) = e^x\) • \(f(x) = ln(1 + x)\) • \(f(x) = x^{1/2}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assig...
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Assignment 13 Use integration by substitution to solve the integral below: \[ \int4e^{-7x}dx\] \[ u = -7x\] \[ du = -7dx\] \[ \frac{du}{-7} = dx\] First substitution \[ \int4e^{u}\frac{du}{-7}\] \[ \int\frac{4}{-7}e^{u}du\] \[ \frac{4}{-7}\int e^{u}du\] \[ \frac{4}{-7} e^{u} + C\] bring back the first substitution to get the final answer: \[ \f...
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STorres Assignment 11
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.) require(car) require(lmtest) require(Hmisc) require(ResourceSelection) #sample data cars <- datasets...
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Assignment 12
WHO Dataset The attached who.csv dataset contains real-world data from 2008. The variables included follow. Variables Country: name of the country LifeExp: average life expectancy for the country in years InfantSurvival: proportion of those surviving to one year or more Under5Survival: proportion of those surviving to five years or more TBF...
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