Publications by Warner Alexis
DATA 605 Assignment 8
Week Assignment 8 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 . Solution The probabiblity that any single \(X_i\) is greater that y \(\frac {k-y}{k}\), so \(k-y\) is greater than y out of ...
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DATA 605 disc Week 7
Exercise 1 page 197 For which of the following random variables would it be appropriate to assign a uniform distribution? (a) Let X represent the roll of one die. Let X represent the number of heads obtained in three tosses of a coin. A roulette wheel has 38 possible outcomes: 0, 00, and 1 through 36. Let X represent the outcome when a roulett...
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Data 605 Assignment 6
Homework 6 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? Lets calculate the combinaisons \(C(n,n) = \frac {n!}{(n- k)!\) C(5,1) C(7,4) C(7,5) # we can draw 1 greenjelly where 1 can have a position out of 5 C1 = choose(5,1)...
4241 sym Python (3592 sym/46 pcs)
Data 605 Assignment 6 Discussion
Exercise 1 page 88 Four people are to be arranged in a row to have their picture taken. In how many ways can this be done? Solution Four can be arrange of the folowing order \(P(n,n) = \frac {n!}{(n- k)!}\) \(P(4,4) = \frac {4!}{4-4}!\) \(P(4,4) = \frac {4*3*2*1}{0}!\) \(P(4,4) = 24\) There are 24 ways to arange 4 people....
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DATA 605 - ASSIGNMENT 5
Problems 1. (Bayesian). 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 without...
5478 sym R (5932 sym/50 pcs)
Data 605 Propabilities Ex1 page 35
Exercise 1 page 35 Let \(\Omega\) be a sample space. Let \(m(a) = 1=2, m(b) = 1=3 , m(c) = 1=6\). Find the probabilities for all eight subsets of \(\Omega\) Solution \(\Omega\) is the space of: \(m(a) = \frac{1}{2}\) \(m(b) = \frac{1}{3}\) \(m(c) = \frac{1}{6}\) \(P(\theta) = m(\theta) = 0\) \(P(a) = m(a) = \frac{1}{2}\) \(P(b) = m(b) = \frac{1}...
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Data 605 Eigenvectors & Image Recognition
Eigenvectors & Image Recognition With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Provide full R code and discussion The eigenvalues can tell you how much variances and diversity in a image. Eigenvalues and eigenvectors are widely used in image processing and signal processing task such as...
2326 sym R (2646 sym/13 pcs) 4 img
DATA 605 - Exercise c25 page 349
{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) Excercise C25 Page 349 Define the linear Transformation of $T: , T:( \[\begin{bmatrix}x_1 & x_2 & x_3\end{bmatrix}\] ) = \[\begin{bmatrix}2x_1-x_2+5x_3 \\ -4x_1+2x_2-10x_3 \end{bmatrix}\] $ Veryfying that T is a linear Transformation if only these T repect this notation: \(T(\vec{u...
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DATA 605 - ASSIGNMENT 3
Assignment 3 we have a matric A \(A = \begin{bmatrix}1 & 2 & 3 & 4\\ -1 &0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3\end{bmatrix}\). We are goijng to reduce the matrix to echelon form R2 <- R2 + R1 R4 <- R4 - 5R1 that will give us this matrix \(A = \begin{bmatrix}1 & 2 & 3 & 4\\ 0 &2 & 4 & 7 \\ 0 & 1 & -2 & 1 \\ 0 & -6 & -17 & -23\end{bma...
3068 sym R (1034 sym/12 pcs)
DATA 605 - Exercise C5
Exercise c15 Working within the vector space C3, determine if matrix b =[4 3 1] is in the subspace of matrix W = {[3 2 3],[1 0 3],[1 1 0],[2 1 3]} . Give me steps by steps calculations Oicture...
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