Publications by Vinayak Kamath
Data605-Week10-HomeWork10-kamath
Home Work 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 t...
765 sym R (243 sym/4 pcs)
Data605-Week11-HomeWork11-kamath
Home Work 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.) #Displaying the car dataset contents: str(cars) ## 'data.frame': 50 obs. of 2 variables: ## $ speed:...
1269 sym R (1613 sym/12 pcs) 4 img
Data605-Week12-HomeWork12-kamath
Home Work 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: propo...
4579 sym R (6609 sym/24 pcs) 2 img
Data605-Week13-HomeWork13-kamath
Home Work 13 Use integration by substitution to solve the integral below. \[ \int 4e^{-7x}dx \] Let u = -7x \[ \frac{du}{dx}=−7 \] \[du=−7dx \] \[dx=\frac{du}{−7}=−\frac{1}{7}du \] \[ = −\frac{4}{7} \int e^udu \] \[ = \frac{4}{7}e^u \] \[ = \frac{4}{7}e^{−7x}+C \] Biologists are treating a pond contaminated with bacteria. The level...
2802 sym R (345 sym/4 pcs) 1 img
Data605-Week14-Discussion14-Kamath
Application of the Derivative Exercise 4.2 #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: 1 cm? 10 cm? 100 cm? #function for claculating the growing rate growing.rate = function(r,h,rate){ Pi = 3.142857 # Aproximation of Pi return(rate / ...
227 sym R (616 sym/7 pcs)
Data605-Week15-HomeWork15-kamath
Home Work 15 #1. Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. \[ ( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 ) \] x <- c(5.6, 6.3, 7, 7.7, 8.4) y <- c(8.8, 12.4, 14.8, 18.2, 20.8) b0 <- round(summary(lm(y ~ x))$coefficients[1], 2) b0 ## [...
2739 sym R (694 sym/12 pcs)
Data605-Final Project-Computational Mathematics
1 Problem 1. Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to N, where N can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of \(\mu =\sigma =\frac{(N+1)}{2}.\) set.seed(246) N <- 6 # N can be any numb...
5135 sym R (25578 sym/95 pcs) 13 img 1 tbl
Data608-Module-01-HomeWork
#Loading additional libraries library(dplyr) library("ggplot2") Principles of Data Visualization and Introduction to ggplot2 I have provided you with data about the 5,000 fastest growing companies in the US, as compiled by Inc. magazine. lets read this in: inc <- read.csv("https://raw.githubusercontent.com/charleyferrari/CUNY_DATA_608/mas...
2013 sym R (9767 sym/36 pcs) 3 img