Publications by Christian Uriostegui
Week 8 Discussion Follow Up
Question A die is rolled three times. Find the probability that the sum of the outcomes is: greater than 9. an odd number. Christian’s Response: Part A: In the code below, I simulated a trail where a die is rolled three times. I chose 10,000 as the number of trails since a large trail will lead to more accuracy. # set the number of trials t...
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Discussion Board Assignment Week 8
Question In one play of a certain game you win an amount X with distribution: \[ px = \begin{pmatrix} 1 & 2 & 3\\ 1/4 & 1/4 & 1/2 \end{pmatrix} \] Using the program NFoldConvolution find the distribution for your total winnings after ten (independent) plays. Plot this distribution. Christian’s Response: To calculate the dis...
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Document
Question The Poisson distribution with parameter λ = .3 has been assigned for the outcome of an experiment. Let X be the outcome function. Find P(X = 0), P(X = 1), and P(X > 1) Christian’s Response: To solve this problem, we can apply the Poisson probability for mass function and substitute the values for X and λ when solving (X=0 and x=1)....
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Discussion Board Assignment Week 6
Question 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? Christian’s Response To solve the problem, we first have to solve for the probability the each president will have died on unique days of the year. Lastly, we subt...
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Discussion Board Assignment Week 5
Problem Let \(\Omega\) = (a,b,c) be a sample space. Let m(a) = 1/2, m(b) = 1/3, and m(c) = 1/6. Find the probabilities for all eight subsets of \(\Omega\). Christian’s Response: To identify all eight subsets, we’ll use this formula: m(A) = \(\Sigma\)m(w) The formula tell us to add the probabilities of all the outcomes for our sample space \(...
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Discussion Board Assignment Week 4
Question # 29 Pg. 460 Let, \(A=\left[ {\begin{array}{cc} 1 & 2 & 1 & 1 \\ 2 & 1 & 1 & 0 \\ 1 & 2 & 1 & 2 \\ 1 & 2 & 2 & 1 \\ \end{array} } \right]\) and let T: \(\mathbb{C^4}\rightarrow\mathbb{C^4}\) be given by \(T\) (x) = Ax. Find K(T). Is T injective? Christian’s Response: Since T is provided by K(T) - N(A), we end up with the followi...
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Data 605 Discussion Board 3
(1) Find the characteristic polynomial of the matrix A: \[ \left[ {\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ \end{array} } \right] \] Christian’s Response: Equation to get characteristic polynomial: \(det(A-\lambda\mathit{I}_n)\) Solve for the following \[ \left[ {\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ \end{array} } \right] - ...
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Data 605 Assignment 2
Problem Set 1 Show that \(A^TA\) does not equal \(AA^T\). (Proof and demonstration) Christian’s Response: When calculating for the transpose of a Matrix, if we have matrix \(A\), then the transpose \(A^T\) will contain the rows of \(A\) as columns. In the matrix created below, we can see that despite \(A^TA\) and \(AA^T\) having the same...
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Lab 1 Class 606
load packages library(tidyverse) ## -- Attaching packages --------------------------------------- tidyverse 1.3.2 -- ## v ggplot2 3.3.6 v purrr 0.3.4 ## v tibble 3.1.6 v dplyr 1.0.8 ## v tidyr 1.2.0 v stringr 1.4.0 ## v readr 2.1.2 v forcats 0.5.1 ## -- Conflicts ------------------------------------------ tidyverse_c...
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Data 606 Lab 2
Load Packages library(tidyverse) ## -- Attaching packages --------------------------------------- tidyverse 1.3.2 -- ## v ggplot2 3.3.6 v purrr 0.3.4 ## v tibble 3.1.6 v dplyr 1.0.9 ## v tidyr 1.2.0 v stringr 1.4.0 ## v readr 2.1.2 v forcats 0.5.1 ## -- Conflicts ------------------------------------------ tidyverse_c...
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