Publications by Joey Bochnik
Final Project
Final Project Problem 1 Using R, set a random seed equal to 1234 (i.e., set.seed(1234)). Generate a random variable X that has 10,000 continuous random uniform values between 5 and 15.Then generate a random variable Y that has 10,000 random normal values with a mean of 10 and a standard deviation of 2.89. # Setting the random seed set.seed(1234) ...
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Week 15 Assignment
Week 15 Assignment Problem 1 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 ) We can use R to find the regression line by putting the points into a matrix and fitting a regression model on the data. x ...
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Week 15 Discussion Page 711 Question 9
Page 711 Problem 9 Find \(f_x, f_y, f_{xx}, f_{yy}, f_{xy} and f_{yx}\). \(f(x,y)=x^2y+3x^2 +4y−5\) \(f_x= x^2y+3x^2+4y-5 \frac{\partial}{\partial x}= 2xy+6x\) \(f_y = x^2y+3x^2+4y-5 \frac{\partial}{\partial y}= x^2+4\) \(f_{xx} =2xy+6x \frac{\partial}{\partial x} = 2y+6\) \(f_{yy} = x^2+4 \frac{\partial}{\partial y} = 0\) \(f_{xy} = 2xy+6x ...
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Week 14 Assignment
Week 14 Assignment This week, we’ll work out some Taylor Series expansions of popular functions. \(f (x) = 1/(1−x)\) \(f(x) = e^x\) \(f (x) = ln(1 + x)\) \(f(x)=x^{(1/2)}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assignment as an R- Markdo...
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Discussion post week 14
Page 496 #31 In Exercises 31 – 32, approximate the value of the given def- inite integral by using the first 4 nonzero terms of the inte- grand’s Taylor series. 31.) \(\int^{\sqrt{\pi}}_{0} sin(x^2) dx\) The Taylor Series for sin(x) is given by : \(\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{(2n+1)!}\) Now substitute in \(x^2\) \(\sum_{n=0}^{\in...
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Week 13 Assignment
Problem 1 Use integration by substitution to solve the integral below \(\int_{}^{} 4e^{-7x} \, dx\) let \(u=-7x\) \(du=-7 dx\) \(dx=-\frac{1}{7}du\) Now substitute back into the integral: \(\int_{}^{} 4e^{u} * -\frac{1}{7} \, du\) \(-\frac{4}{7} \int_{}^{} e^{u} \, du=\) \(=-\frac{4}{7}e^u + c\) Substitute u = -7x \(=-\frac{4}{7}e^{-7x} + c\) Pro...
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Week 13 Discussion
Page 179 Question 10 A boat is being pulled into a dock at a constant rate of 30ft/min by a winch located 10ft above the deck of the boat. At what rate is the boat approaching the dock when the boat is: 50 feet out? 15 feet out? 1 foot from the dock? What happens when the length of rope pulling in the boat is less than 10 feet long? Part A The pi...
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Week 12 Assignment
Week 12 Assignment The attached who.csv dataset contains real-world data from 2008. The variables included follow. 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 TBFree: propor...
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Document
library(Lahman) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union library(ggplot2) # Load team data teams_data <- Teams # Select only the relevant columns we will sel...
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Week 11 Assignment
Week 11 Assignment Using the “cars” data set 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.) The cars data set is built into R and can be accessed easily through the variable “cars” library(d...
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