Publications by Jagdish Chhabria
Document
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-Markdown document. f(x) = 1/(1 - x) Taylor’s formula states that: \[f(x) = \sum_{n=1}^{\infty} f^n(0...
2352 sym R (456 sym/8 pcs)
Document
1. Use integration by substitution to solve the integral below. $$4e^{-7x} , dx = 4 e^{-7x} , dx \ = 4 (e^{-7x}/-7)+C = -4/7, e^{-7x} + C $$ 2. Biologists are treating a pond contaminated with bacteria. The level of contamination is changing at a rate of: \[ dN/dt = - 3150/t^4 - 220 \] bacteria per cubic centimeter per day, where t is the number...
4413 sym R (333 sym/11 pcs) 1 img
Publish Document
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() # Loading data(cars) #?cars # Check dimensions dim(cars) ## [1] 50 2 # Inspect column names names(cars) ## ...
2149 sym R (1866 sym/17 pcs) 6 img
Publish Document
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 (timid...
2620 sym R (717 sym/4 pcs)
Document
The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by Yn on the nth day of the year. Finn observes that the differences Xn = Yn+1 ??? Yn appear to be independent random variables with a common distribution having mean mu = 0 and variance sigma^2 = 1/4. If Y1 = 100, estimate the probability that Y365 is: ...
1860 sym R (854 sym/10 pcs) 2 img
Document
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? Since the lifetime of each bulb follows an exponential distribution, and the expected lifetime is 1000 hours, we set mu = 1000. For an exponential distribution, the intensity paarmeter lambda ...
1775 sym
Document
A die is rolled three times. Find the probability that the sum of the outcomes is (a) greater than 9. (b) an odd number. library(tidyverse) ## -- Attaching packages ----------------------------------------------------------- tidyverse 1.2.1 -- ## v ggplot2 3.1.1 v purrr 0.3.2 ## v tibble 2.1.1 v dplyr 0.8.0.1 ## v tidyr 0.8...
128 sym R (1555 sym/8 pcs)
Document
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. We are looking to find the probability that Y is less than or equal to some value s, which translates to the event that one of the draws from the ...
2484 sym R (789 sym/26 pcs)
Document
A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box,what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. p.red<-54/(54+9+75) p.blue<-75/(54+9+75) p.red_or_blue <- p.red + p.blue round(p.red_or_blue,4)...
5806 sym R (1796 sym/28 pcs)
Publish Document
Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions. Note that the point (B,C) is then chosen at random in the unit square. Find the probability that: # We simulate 100000 trials for selection of number B from the interval 0 to 1, with equal prob...
713 sym R (690 sym/21 pcs) 2 img