Mathématiques

This document provides a comprehensive guide on statistical computations in R, detailing descriptive statistics functions (mean, median, etc.), handling missing data, and probability distribution manipulations. Examples use R's built-in datasets (e.g., `cars`) to demonstrate the syntax and outputs of functions including `mean`, `var`, and `cor`. Instructions on generating random numbers are also included, with coverage of advanced tools like `summary`, `xtabs`, and `ftable` for analyzing categorical data. Methods are presented in a structured manner to facilitate statistical analysis and da...

This document provides an in-depth discussion of logistic regression, particularly when the dependent variable is binary and independent variables may be qualitative or quantitative. It details the methodology for model specification, interpretation of coefficients, parameter estimation, and tests such as the likelihood ratio test for determining variable significance. Applications highlighted include predicting outcomes in health scenarios and identifying factors influencing drug relapse, using both single-variable and multiple-variable logistic regression models, supported by real-world c...

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This document contains practical exercises covering multiple statistical concepts including probability distributions, estimation techniques, calculation of confidence intervals, hypothesis testing, and statistical properties (bias and efficiency). The methodology emphasizes working with real-world data through sampling, and the purpose is to answer questions using inferential statistics such as means, proportions, and standard deviations. Findings include applying theoretical models (e.g., Binomial and Normal distributions) and performing estimations of unknown parameters based on sample d...

This document provides mathematical reference tables and equations for statistical distributions, including normal, Student's t, Chi-square, and Fisher-Snedecor distributions. It includes tables for probability values and thresholds for significance testing in various scenarios. The core methodology integrates probability theory and statistical computations to assess distribution behavior under different parameters. These findings are critical for performing accurate statistical tests in academic and professional settings.

This document provides a detailed explanation of continuous random variables, including their definitions, properties, and applications. It explores key concepts such as probability density functions, cumulative distribution functions, expectation, and variance. The document dedicates a section to the Normal distribution, discussing its natural occurrence, properties, parametrization, and transformations. Additionally, practical calculation examples and graphical interpretations are extensively presented to enhance understanding.

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This document includes a set of exercises focusing on probability distributions, statistical inference, and real-world applications. It introduces problems involving the calculation of probability distributions, cumulative distribution functions, expected values, and variances. Practical scenarios such as machine precision in production lines and demand forecasting using normal distributions are analyzed. The document aims to strengthen statistical analytical skills through applied problems.

This document presents a comprehensive statistical analysis of a contingency table, focusing on data input into SPSS for frequency calculations. It involves conducting a Chi-squared test for independence, performing a Correspondence Analysis (CA) to evaluate row and column profiles, and calculating total inertia. Interpretation of dependency between observed and theoretical frequencies, contributions of income and class-standing modes, and factor maps is provided with justification of the number of axes to retain.