Publications by Ahmed Elsaeyed
AElsaeyed_Discussion9
Page 36 Question 12 Test your conclusions in Exercise 11 by computer simulation. First choose 364 numbers Xi with density f(x) = normal(x, 0, 1/4). Now form the sum Y365 = 100 + X1 + X2 + · · · + X364, and repeat this experiment 200 times. Make up a bar graph on [50, 150] of the results, superimposing the graph of the approximating normal densit...
680 sym 4 img
AElsaeyed_Homework9
Question 1 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 \(Y_1\) = 100, estimate th...
2118 sym
AElsaeyed_Homework8
Question 11 p303 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? In this question we are interested in the lifetime of an individual lightbulb. If \(\lambda\) represents the rate parameter of the distribution then the mean of the exponential ...
2224 sym
AElsaeyed_Home
Question 1 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? We use the formula: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] For this case, \(n = 7\) (total red jellybeans) and \(k = 5\) (jellybeans to be withdrawn), so: \[ C(7, 5) = \frac{7...
2095 sym
AElsaeyed_Discussion6
Five people get on an elevator that stops on five floors. Assuming that each has an equal probability of going to any one floor, find the probability that they all get off on different floors. Given: - The number of people \(n = 5\). - The number of floors \(n = 5\). The probability \(P\) that all five people get off on different floors is calculat...
1194 sym
AElsaeyed_Homework5
Question 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 the d...
2580 sym
AElsaeyed_Discussion5
Question 1, Page 12 Modify the program CoinTosses to toss a coin n times and print out after every 100 tosses the proportion of heads minus 1/2. Do these numbers appear to approach 0 as n increases? Modify the program again to print out, every 100 times, both of the following quantities: the proportion of heads minus 1/2, and the number of heads mi...
573 sym
AElsaeyed_HW4
The below code finds the “eigenshoes” from a group of images of shoes. This process makes sense to me on a procedural level- we want to find the principal components that describe the majority (or 80%) of these shoes. I did get a little lost trying to follow along what the code was doing, but I will try my best to explain each step. library(doP...
1286 sym R (3908 sym/27 pcs) 4 img
AElsaeyed_Discussion4
Find the matrix representation of: T: \(T: C^3 -> C^4, T \left(\begin{bmatrix} x \\ y \\ z \end{bmatrix} \right) = \begin{bmatrix} 3x + 2y +z \\ x + y + z \\ x-3y \\ 2x + 3y + z \end{bmatrix}\) The matrix on the right side can be written as: \(\begin{bmatrix} 3x \\ x \\ x \\ 2x \end{bmatrix} + \begin{bmatrix} 2y \\ y \\ -3y \\ 3y \end{bmatrix} + \b...
1103 sym
Aelsaeyed_HW3
Problem Set 1 1. What is the rank of the matrix A? A = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -1 & 1 \\ 5 & 4 & -2 & -3 \\ \end{bmatrix}\) Answer: I will find the reduced row-echelon form in order to determine the rank. Here I will do it by hand and then use the RREF function from pracma to confirm. Add row 1 to row 2 A = \...
6681 sym