Publications by Luz Melo
Theory I: Final Exam
Theory I: Final Exam Luz Melo 2022-12-13 Instructions The final exam will be a one-on-one oral exam with the instructor. Please prepare solutions to the following is a set of questions. During the oral exam, the instructor will ask a series of questions covering topics from the course and the questions. For example, the instructor may ask: Pl...
14677 sym Python (10679 sym/83 pcs) 10 img 5 tbl
Simulation Study: Central Limit Theorem
Simulation Study: Central Limit Theorem Luz Melo 2022-12-02 Introduction The central limit theorem is an important computational short-cut for generating and making inference from the sampling distribution of the mean. You’ll recall that the central limit theorem short-cut relies on a number of conditions, specifically: Independent observati...
3327 sym 1 img
The Probability of Victory: How Often Does the Better Team Win the World Series?
The world series is a first to 4 wins or best of 7 match-up between the champions of the American and National Leagues of Major League Baseball. In this assignment, we are going to explain probability calculations related to the world series and first to k win random variables. Setup: Suppose that the Braves \((B)\) and the Yankees \((Y)\) are...
10504 sym Python (2585 sym/25 pcs) 2 img 2 tbl
Practice Problems on Distribution Functions and Probability Calculations
Practice Problems on Distribution Functions and Probability Calculations Luz Melo 10/19/2022 1. Suppose the random variable \(X\) has density \(1.5t^{(0.5)}\) on \((0, 1)\), \(0\) elsewhere. Find \(F_X(0.5)\) Mathematical Solution: Our density function is given by \[ \begin{aligned} f_X(t)&= P(X=t)\\ &=\begin{cases} 1.5t^{0....
7429 sym 7 img
Which Quantiles of a Continuous Distribution Can One Estimate with More Precision?
Introduction The median is an important quantity in data analysis. It represents the middle value of the data distribution. Estimates of the median, however, have a degree of uncertainty because the estimates are calculated from a finite sample and the data distribution of the underlying data is generally unknown. One important roles of a data...
6145 sym 12 img
Linear Mixed Effects Models in Longitudinal Health Studies
Linear Mixed Effects Models in Longitudinal Health Studies Luz Melo 2024/08/22 Introduction In this article, we will recreate the results of three case studies of the book Applied Longitudinal Analysis, 2nd Edition, by Garrett Fitzmaurice, Nan Laird & James Ware. In particular, we are interested in understanding the results of chapter 8: Linea...
17306 sym Python (22546 sym/54 pcs) 7 img 4 tbl
Is Playing Roulette with The Martingale Betting Strategy a Good Idea?
Is Playing Roulette with The Martingale Betting Strategy a Good Idea? If there is one thing we all know about casinos is that the house always wins. However, this doesn’t stop many from trying to outsmart the system. In this article, we will for one and for all determine whether or not playing the roulette with the martingale betting strateg...
8114 sym 3 img 1 tbl
Linear Mixed-Effects Models in Longitudinal Health Studies
Linear Mixed-Effects Models in Longitudinal Health Studies Luz Melo 2024-07-26 Introduction In this article, we will recreate the results of three case studies of the book Applied Longitudinal Analysis, 2nd Edition, by Garrett Fitzmaurice, Nan Laird & James Ware. In particular, we are interested in understanding the results of chapter 8: Linea...
14339 sym Python (23135 sym/53 pcs) 8 img 4 tbl
Solving the Birthday Paradox: Simulation and Analysis
Solving the Birthday Paradox: Simulation and Analysis Luz Melo 9/26/2022 Suppose we are asked the following question: In a class of N individuals, what is the probability that at least two students will share a birthday?. In this article we will explain how to answer the birthday problem with both simulation and analytic tools. We will assume ...
6566 sym 4 img 2 tbl
Document
Linear Mixed Effects Models in Longitudinal Health Studies Luz Melo 2024/08/22 Introduction In this article, we will recreate the results of three case studies of the book Applied Longitudinal Analysis, 2nd Edition, by Garrett Fitzmaurice, Nan Laird & James Ware. In particular, we are interested in understanding the results of chapter 8: Linea...
17309 sym Python (23604 sym/56 pcs) 7 img 5 tbl