Publications by Johnny Rodriguez
Data 605 Discussion 7
Page 200, Question 20 An advertiser drops 10,000 leaflets on a city which has 2000 blocks. Assume that each leaflet has an equal chance of landing on each block. What is the probability that a particular block will receive no leaflets? We use the Poisson distribution because: number of times an event happens occurs in fixed interval of time event...
736 sym
Data 605 Homework Week 7
1 - Min / Max Distribution 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. The Min / Max Distribution is \(P(Y \leq y) = 1 - \left(\frac{k - y}{k}\right)^n\) 2a - Geometric Distribution Your org...
2832 sym Python (4730 sym/28 pcs) 4 img
Data 605 Homework 6
1. Jelly Beans 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? These are the two conditions where green < 2 and allowing for a drawing of 5 jelly beans. The outcomes of each are added to count the mutually exclusive events. # calcul...
3750 sym Python (4052 sym/28 pcs)
Data 605 Week 6
What is the probability that at least 2 of the presidents of the United States have died on the same day of the year? If you bet this has happened, would you win your bet? Page 88 #4 To calculate this, we first calculate the probabailities that presidents all died on different days. We then use the complement to calculate the probability that they ...
489 sym
Data 605 Homework 5 - Distributions
1. Bayesian Calculation for HIV Test A new test for multinucleoside-resistant (MNR) human immunodeficiency virus type 1 (HIV-1) variants was recently developed. The test maintains 96% sensitivity, meaning that, for those with the disease, it will correctly report “positive” for 96% of them. The test is also 98% specific, meaning that, for those...
12082 sym Python (10297 sym/68 pcs)
Data 605 Discussion Week 4
Verify T is a linear transformation. C25, Page 349 For a transformation to be linear, it must satisfy both additivity and homogeneity. \(T: \mathbb{C}^3 \rightarrow \mathbb{C}^2\) \[ T\left(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\right) = \begin{bmatrix} 2x_1 - x_2 + 5x_3 \\ -4x_1 + 2x_2 - 10x_3 \end{bmatrix} \] The matrix representation o...
1461 sym
Data 605 PCA Eigen Shoes
Prep Environment Package and Library Load #install.packages("imager") #install.packages("BiocManager") #BiocManager::install("EBImage") #install.packages("ggplot2") # Load the libraries library(imager) library(jpeg) library(EBImage) library(ggplot2) Read the image files # Specifies the file path to the directory where JPG images are stored. fold...
641 sym Python (10335 sym/17 pcs) 8 img
Data 605 Assignment 3 EigenValues & EigenVectors
What is the rank of the matrix A? The rank is 4. Since its only necessary to RREF until the Lower Triangle has been calculated, we can stop without needing to go all the way to RREF. The rank is equal to all non-zero rows. [ \[\begin{alignat*}{2} \left(\begin{array}{rrrr} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -2 \end{arr...
8386 sym
Week 2 Discussion
Page 278 M15 Given the matrix \(\small B = \begin{pmatrix} 2-x & 1 \\ 4 & 2-x \end{pmatrix}\) , find all values of x that are solutions of det(B) = 0. Calculate the determinant of a 2 x 2 matrix using the formula det(B) = ad - bc Therefore: det(B) = (2−x)(2−x)−(1)(4) Simplify the expression det(B) = (2−x)(2−x)−(1)(4) det(B) = (2-x)^2 ...
544 sym
Data 608 Story 4
How much do Data Science roles get paid in the US? Data Sources The data used to answer the question is taken from Glassdoor via Kaggle. The data was scrapped from Glassdoor and posted to the site. The data collected represent 2021 Job Listings with salary and location information for Data Science related careers. Please note the dataset did not c...
1655 sym 4 img