Publications by Mohamed Hassan-El Serafi
Data 605 HW13
1. Use integration by substitution to solve the integral below. \[ \int { 4{ e }^{ -7x }dx } \] Selecting \(u\) to be the \(g(x)\) inside \(f(g(x))\) \[ u=-7x\\ du=-7dx\\ -\frac{du}{7}=dx \] Substitute \(dx\) with \(du\) (reverse chain rule) \[ \frac{-4}{7} \int { { e }^{ u }du } \\ = \frac{-4}{7}e^{u}+C\\ = \frac{-4}{7}e^{-7x}+C \] Answer: \(\frac...
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Data 605 HW12
1. Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error,and p-values only. Discuss whether the assumptions of simple linear regression met. library(tidyverse) data <- read.csv("/Users/mohamedhassan/Downloads/who.csv") summary(data) ## ...
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Data 605 Discussion 12
library(tidyverse) library(GGally) set.seed(123) data1 <- read_csv("/Users/mohamedhassan/Downloads/Sleep_Efficiency.csv") summary(data1) ## ID Age Gender ## Min. : 1.0 Min. : 9.00 Length:452 ## 1st Qu.:113.8 1st Qu.:29.00 Class :character ## Median :226.5 Median :40.00 Mode :chara...
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Data 605 HW11
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(tidyverse) summary(cars) ## speed dist ## Min. : 4.0 Min. : 2.00 ## 1st Qu.:12.0 ...
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Data 605 HW10
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...
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Data 605 HW9
Page 363, Question 11 The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by \(Y_n\) on the nth day of the year. Finn observes that the differences \(X_n = Y_n+1\) − \(Y_n\) appear to be independent random variables with a common distribution having mean \(µ\) = 0 and variance \(σ^2\) = 1/4. If \(Y_1\) =...
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Data 608 Story 4
library(chromote) library(htmltools) library(rvest) library(readxl) library(plotly) library(leaflet) library(sf) library(ggplot2) library(maps) library(RColorBrewer) # lots of color palettes for these kind of charts library(data.table) # for sorting by key library(mapproj) #coord_maps() needed this #library(lattice) #library(vegalite) library(tidyv...
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Data 605 HW8
Page 303 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? light_bulbs <- 100 lifetime <- 1000 lambda_rate <- light_bulbs/lifetime 1/lambda_rate ## [1] 10 Assume that X1 and X2 are independent random variables, each having an exponential de...
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Data 608 Story 4
library(chromote) library(htmltools) library(rvest) library(readxl) library(plotly) library(leaflet) library(sf) library(ggplot2) library(maps) library(RColorBrewer) # lots of color palettes for these kind of charts library(data.table) # for sorting by key library(mapproj) #coord_maps() needed this #library(lattice) #library(vegalite) library(tidyv...
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Data 605 HW7
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. I’ll use an example where \({X1, X2, X3, X4}\) will be the number of independent random variables, \(n = 4\), uniformly distributed on integers ...
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