Publications by Tony Mei
Data 605 Discussion 16
In Exercises 7 – 14, give the domain and range of the multi-variable function. \[\ f(x, y) = \sqrt{9-x^2-y^2}\] \[\ 0 \leq 9-x^2-y^2\] \[\ x^2-y^2 \leq 9\] Domain \[\ D = {(x,y) x^2-y^2 \leq 9} \] Square root ensures that all output is \(\ \geq0\). \(\ x = 0, y = 0\) \(\ f(0, 0) = \sqrt{9-(0)^2-(0)^2}\) \(\ f(0,0) = 3\) Therefore the range R ...
375 sym
Data 605 Assignment 14
Objective ASSIGNMENT 14 - TAYLOR SERIES IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS - 2014 This week, we’ll work out some Taylor Series expansions of popular functions. 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 a R-Markdow...
1531 sym R (29 sym/1 pcs)
Data 605 Discussion 15
Key Idea 8.8.1 gives the nth term of the Taylor series of common functions. In Exercises 3 – 6, verify the formula given in the Key Idea by finding the first few terms of the Taylor series of the given function and identifying a pattern. \[\ f(x) = sin x; c = 0\] Taylor series of f(x) = sin(x) at = 0 is \[\sum_{n=0}^{\infty} (-1)^n\frac{x^{2n...
956 sym
Data 605 Assignment 13
1. Use integration by substitution to solve the integral below. \[\int 4e^{-7x} dx\] Let \(\ u = -7x\) \[\frac{du}{dx} = -7\] \[\ du = -7dx\] \[\ dx = \frac{du}{7}\] \[\int 4e^{u} * \frac{du}{-7}\] \[\frac{1}{-7}\int 4e^{u} * {du}\] \[\frac{1}{-7}[4e^{u}] + c\] \[\frac{1}{-7}[4e^{-7x}] + c\] \[\frac{4}{-7}[e^{-7x}] + c\] 2. Biologists are treati...
2824 sym R (233 sym/3 pcs) 1 img
Data 605 Assignment 12
Dataset 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 t...
2882 sym R (4083 sym/25 pcs) 5 img
Data 605 Assignment 11
Objective 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.) Data Visualization # cars data head(cars) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 7 4...
1385 sym R (1092 sym/12 pcs) 4 img
Data 605 Discussion 12
Objective Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? The dataset we will be using is Orange which displays the growth of orange trees. We want to find out if the increasing age of the tree affects the circumference of the trees. Data Visualization he...
718 sym R (1087 sym/8 pcs) 4 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 (timi...
1067 sym R (217 sym/2 pcs)
Data 605 Discussion 9
Let S200 be the number of heads that turn up in 200 tosses of a fair coin. Estimate \(\ 1/√2π*e^(−1/2)\) e=2.71828 clt=1/sqrt(2*pi)* (e**(-1/2)) \(\ P(S200 = 100)\) n=200 p=1/2 q=1/2 n*p ## [1] 100 ans=sqrt(n*p*q) x100=(100-(n*p))/ans x100 ## [1] 0 x100*clt ## [1] 0 \(\ P(S200 = 90)\) n=200 p=1/2 q=1/2 n*p ## [1] 100 ans=sqrt...
176 sym R (375 sym/19 pcs)
Data 605 Homework 8
Page 303 #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? (See Exercise 10.) \(\ E[Xi]=1/λi\) \(\ λi= λ1+...+λ100 = 100/1000 = 1/10\) \(\ E[Xi]=1/(1/10)\) \(\ E[Xi]= 10\) 10 hours Page 303 #14 Assume that X1 and X2 are independent ...
1406 sym