Publications by Brian Singh

BrianSingh_Data624_HW2

16.02.2024

3.1 Consider the GDP information in global_economy. Plot the GDP per capita for each country over time. Which country has the highest GDP per capita? How has this changed over time? library(fpp3) ## Warning: package 'fpp3' was built under R version 4.2.3 ## ── Attaching packages ─────────────────────�...

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BrianSingh_Data624_HW1_Spring24

05.02.2024

1. Explore the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec. Use ? (or help()) to find out about the data in each series. library(fpp3) ## ── Attaching packages ─────────────────────────────────────�...

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BrianSingh_Data605_Final_Fall2023

16.12.2023

library(tidyverse) ## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ── ## ✔ dplyr 1.1.3 ✔ readr 2.1.4 ## ✔ forcats 1.0.0 ✔ stringr 1.5.0 ## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1 ## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0 ## ...

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BrianSingh_Data605_Hw14

04.12.2023

\(f(x) = \frac{1}{1-x}\) Derivatives: \(f^0(c) = \frac{1}{(1-c)}\) \(f'(c) = \frac{1}{(1-c)^2}\) \(f''(c) = \frac{2}{(1-c)^3}\) \(f'''(c) = \frac{6}{(1-c)^4}\) The Taylor series would be defined as \(f(x) = \frac{1}{(1-c)0!}(x-c)^0 + \frac{1}{(1-c)^2*1!}(x-c)^1 + \frac{2}{(-c)^3*2!}(x-c)^2 + \frac{6}{(1-c)^4*3!}(x-c)^3...+\sum_{n=0}^\infty \fr...

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BrianSingh_Data605_HW13

29.11.2023

0.1 1. Use integration by substitution to solve the integral below. \(\int4e^{-7x}dx\) \(u =-7x\) \(\frac{du}{dx} = -7\) \(dx = -\frac{1}{7}du\) \(-\frac{4}{7}\)\(\int e^{u}du\) \(-\frac{4}{7}e^{u}\) Sub -7x for u: \(-\frac{4}{7}e^{7x}\) 0.2 2. Biologists are treating a pond contaminated with bacteria. The level of contamination is changin...

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BrianSingh_Data605_Hw12

20.11.2023

0.1 Load Libraries and Data library(tidyverse) ## Warning: package 'tidyverse' was built under R version 4.2.3 ## Warning: package 'ggplot2' was built under R version 4.2.3 ## Warning: package 'tibble' was built under R version 4.2.3 ## Warning: package 'tidyr' was built under R version 4.2.3 ## Warning: package 'readr' was built under R version 4...

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BrianSingh_Data605_HW11

12.11.2023

1 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.) library(ggplot2) library(tidyverse) ## ── Attaching core tidyverse packages ─────────────�...

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BrianSingh_Data605_HW10

06.11.2023

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 time (timid stra...

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BrianSingh_Data605_HW9

31.10.2023

1. 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 µ = 0 and variance σ2 = 1/4. If Y1 = 100, estimate the probability that Y365 is (a) ...

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BrianSingh_Data605_HW8

25.10.2023

Page 303 Q. 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? lambda <- 1/1000 #rate bulbs <- 100 #num bulbs first_bulb_time <- -log(1 - 1/100) / lambda first_bulb_time ## [1] 10.05034 10 hours Page 303 Q. 14 Assume that X1 and X2 ar...

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