Publications by Amit Kapoor
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...
1138 sym R (210 sym/2 pcs)
Data 605 - Discussion 10
Page 414 Ex 7. Find the matrices \(P^2\), \(P^3\), \(P^4\), and \(P^n\) for the Markov chain determined by the transition matrix P = \(A = \left( \begin{matrix} 1&0 \\ 0&1 \end{matrix} \right)\). Do the same for the transition matrix P = \(A = \left( \begin{matrix} 0&1 \\ 1&0 \end{matrix} \right)\). Interpret what happens in each of these process...
821 sym R (803 sym/22 pcs)
Data 607 - Tidyverse Create
Assignment Using one or more TidyVerse packages and any dataset from fivethirtyeight.com or Kaggle, the task is to create a programming sample “vignette” that demonstrates use of one or more of the capabilities of selected TidyVerse package. Getting started Lets load tidyverse package first. It includes readr, dplyr, tidyr, ggplot2, stringr,...
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Data 605 - Discussion 9
A surveying instrument makes an error of −2, −1, 0, 1, or 2 feet with equal probabilities when measuring the height of a 200-foot tower. (a) Find the expected value and the variance for the height obtained using this instrument once. act_height <- 200 exp_err <- 1/5*(-2+(-1)+0+1+2) # expected value for the height obtained using this instrum...
392 sym R (630 sym/6 pcs)
Data 605 - Assignment 8
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? The density of minimum value among n independent random variables with an exponential density has mean \(\mu\)/n. mu <- 1000 n <- 100 exp_time <- mu/n exp_time ## [1] 10 14. Assume that...
2302 sym R (218 sym/10 pcs)
Data 605 - Discussion 8
Chapter 8 Ques 16: Let Z = X/Y where X and Y have normal densities with mean 0 and standard deviation 1. Then it can be shown that Z has a Cauchy density. (a) Write a program to illustrate this result by plotting a bar graph of 1000 samples obtained by forming the ratio of two standard normal outcomes. Compare your bar graph with the graph of t...
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Data 607 - Assignment 7
Introduction In this assignment, data about 3 books is stored in 3 different format files; XML, JSON and HTML. These 3 files can be accessed through this github link. The task is to load the information from each of the three sources into separate R data frames and compare them. library(XML) library(jsonlite) library(RCurl) ## Loading required pa...
2158 sym R (4659 sym/12 pcs) 3 tbl
Data 605 - Assignment 7
1. Let X1, X2, . . . , Xn be n mutually independent random variables, each of which is uniformly distributed on the integers from 1 to k. Let Y denote the minimum of the Xi’s. Find the distribution of Y. Given Y denote the minimum of the Xi’s. P(Y) = min(X1, X2, X3, ….. Xn) Assuming each Xi has k possibilities: 1,2,3,….k, then total numbe...
2068 sym R (1235 sym/24 pcs)
Data 605 - Discussion 7
Chapter 5, Page 197, Ques 7 A die is rolled until the first time T that a six turns up. What is the probability distribution for T? Per geometric distribution P(T = j) = \({q}^{j-1}\)\(\times{p}\) where q=1-p Here p = 1/6 so q = 1-1/6 = 5/6 So probability distribution for T is P(T=j) = \({(\frac{5}{6})}^{j-1}\)\(\times{\frac{1}{6}}\) for j = 1,...
665 sym R (98 sym/1 pcs) 1 img
Data607 - Project2C
About the data The data considered here is a dataset which has five colors cloths and their reaction to cooling and heating in every 10 minutes. Below are the variables description in the data color - Cloth color minute.0 - initial reaction minute.10 - temp after 10th minute (in Farenheit) minute.20 - temp after 20th minute (in Farenheit) minute...
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