Publications by Folorunsho Atanda
FA_LF_HW10
library(markovchain) ## Warning: package 'markovchain' was built under R version 4.3.3 ## Package: markovchain ## Version: 0.9.5 ## Date: 2023-09-24 09:20:02 UTC ## BugReport: https://github.com/spedygiorgio/markovchain/issues Question 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...
2446 sym R (1892 sym/7 pcs)
FA_LF_HW8
Q11. A company buys 100 light bulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? Ans. From Q10. we know that for \(n\) independent variables, which has an exponential density with mean \(\mu\), the mean of the minimum value of any of the independent variable is \(...
3155 sym
FA_LF_Discussion8
Q6 Pg 321 and 322 If X is normally distributed, with mean \(\mu\) and variance \(\sigma^2\), find an upper bound for the following probabilities, using Chebyshev’s Inequality. Note, from Chebyshev’s Inequality: \[ \begin{aligned} P(|X - \mu| \geq k) \leq \frac{\sigma^2}{k^2} \end{aligned} \] a. \[ \begin{aligned} P(|X - \mu| \geq \sigma...
801 sym
FA_LF_HW6
Q1. A bag contains 5 green and 7 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? Formula: \[ \begin{aligned} C(n, r) = \frac{n!}{(n - r)!*r!} \end{aligned} \] Number of permutation of 5 jellybeans where at most 1 are green: \[ \begin{aligned} C(5, 0)*C...
7830 sym
FA_LF_DiscussionWK6
Q11. Pg97. There are n applicants for the director of computing. The applicants are interviewed independently by each member of the three-person search committee and ranked from 1 to n. A candidate will be hired if he or she is ranked first by at least two of the three interviewers. Find the probability that a candidate will be accepted if th...
1544 sym
FA_LF_DiscussionWK5
suppressWarnings( library(tidyverse) ) ## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ── ## ✔ dplyr 1.1.4 ✔ readr 2.1.5 ## ✔ forcats 1.0.0 ✔ stringr 1.5.1 ## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1 ## ✔ lubridate 1.9.3...
131 sym R (2097 sym/7 pcs) 1 img
FA_LF_HW5
suppressWarnings( library(tinytex) ) Q1 \[ \begin{align} P(Positive \lvert Disease) &= 0.96 \: \rightarrow \: Sensitivity \\ P(Negative \lvert No \: Disease) &= 0.98 \: \rightarrow \: Specificity \\ P(Diseased) &= 0.001 \: \rightarrow \: Prevalence \end{align} \] 1a \[ P(Disease \lvert Positive) = \frac{P(Positive \lvert Disease)P(...
3061 sym R (4166 sym/65 pcs)
FA_LF_HW4
HW4 With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Going to start with one shoe library(jpeg) library(EBImage) Plot function plot_jpeg = function(path, add=FALSE) #initialize function { require('jpeg') jpg = readJPEG(path, native=T) # read the file res = dim(jpg)[2:1] # get the ...
1112 sym R (4748 sym/20 pcs) 3 img
Data 605 Discussion Week 4
Load library suppressWarnings( library(tinytex) ) Question C26 Pg 349 Verify that the fuction below is a linear transformation \[T: P_2 \rightarrow C^2, T(a + bx + cx^2) = \begin{bmatrix}2a - b \\b + c \end{bmatrix}\] For a function to be a linear transformation: \[ \begin{aligned} 1&. \: T(u_1 + u_2) = T(u_1) + T(u_2) \: \forall \: u_1, ...
2074 sym R (40 sym/1 pcs)
FA_LF_HW3
Load library suppressMessages( library(tidyverse), library(tinytex) ) ## Warning: package 'tinytex' was built under R version 4.3.2 ## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ── ## ✔ dplyr 1.1.2 ✔ readr 2.1.4 ## ✔ forcats 1.0.0...
5631 sym R (1529 sym/18 pcs)