Publications by Gregg Maloy
Data 605 Discussion Week 14
In Exercises 21, write out the first 5 terms of the Binomial series with the given k-value. 21. k = 1/2 library(Ryacas0) x <- Sym("x") expression <- (1 + x)^4 expression_final <- Expand(expression) print(expression_final) ## yacas_expression(x^4 + 4 * x^3 + 6 * x^2 + 4 * x + 1) term 1: x^4 term 2: 4x^3 term 3: 6x^2 term 4: 4x term 5: 1...
173 sym R (177 sym/2 pcs)
Data 605 Assignment Week 14
Question This week, we’ll work out some Taylor Series expansions of popular functions. We’ll explore the following functions and compute their Taylor Series expansions: \(f(x) = 1/(1 - x)\) \(f(x) = e^x\) \(f(x) = \ln(1 + x)\) \(f(x) = x^{1/2}\) For each function, we will only consider its valid ranges as indicated in the notes when computin...
447 sym R (535 sym/8 pcs)
Data 605 Assignment Week 13
Question 1 Use integration by substitution to solve the integral below. \[ \int 4e^{-7x} \, dx \] Answer u=-7x du=-7dx dx=-(1/7)du \[ \begin{align*} \int 4e^{-7x} \, dx &= \int 4e^u \frac{-1}{7}du \\ &= -\frac{4}{7} \int e^u \, du \\ &= -\frac{4}{7} e^u + C \quad \\ &= -\frac{4}{...
1632 sym R (943 sym/12 pcs)
Data 605 Discussion Week 13
Using R, provide the solution for any exercise in either Chapter 4 or Chapter 7 of the calculus textbook. If you are unsure of your solution, post your concerns. Question 3, page 179 3. Water flows onto a flat surface at a rate of 5cm3/s forming a circular puddle 10mm deep. How fast is the radius growing when the radius is: (a) 1 cm? (b) 10 cm...
373 sym
Data 605 Assignment Week 12
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: proportion of the popu...
12852 sym R (4532 sym/21 pcs) 5 img 2 tbl
Data 605 Discussion Week 12
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? Introduction I decided to use the ‘Ir...
4675 sym 3 img
Data 605 Assignment Week 11
Assignment 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). Part 1: Hypothesis Null Hypothesis (H₀): There is no relationship between the speed of the cars’ and t...
5335 sym Python (1908 sym/13 pcs) 7 img
Data 605 Discussion Week 11
Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? Introduction Last semester, I conducted various analysis on maternal morbidity which showed that maternal mortality was on the increase for all racial/ethnic groups in the United States, as well as NYC. I ...
3009 sym R (4961 sym/12 pcs) 5 img
Data 605 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 (a) he bets 1 dollar each time (tim...
700 sym R (3137 sym/14 pcs)
Data 605 Discussion Week 10
Introduction to Probability, Grinstead, C. Snell, J., 1997 Page 443 Question 5 Question Find the fixed probability vector for each of the following regular matrices \(\begin{pmatrix}0.75 & 0.25 \\0.5 & 0.5 \\\end{pmatrix}\) #install.packages("markovchain") library(markovchain) matrix <- matrix(c(.75, .25, .5, .5), byrow = TRUE, nrow = 2) ch...
375 sym R (936 sym/6 pcs)