DALMINE
Overview
Date/time interval
Syllabus
Course Objectives
The course has two goals. Firstly, it provides students with the theory of descriptive statistics, of probability and inferential statistics. Secondly, it teaches students how to use statistics for analyzing real data by using Excel. Special attention will be given to engineering applications.
Course Prerequisites
Program of the teaching "Analisi matematica I" (first semester).
Basic knowledge of a statistical software (chosen by the teacher).
Teaching Methods
Theory lessons (32 hours) and praticals (16 hours) are frontal. For the praticals, the students are divided in groups.
The teaching material (slides, exercises and any other additional material) for exam preparation are uploaded by the teachers on the e-learning page of the course.
Assessment Methods
Two lab tests using the pc, each consisting of theory and exercises questions. Students are expected to solve questions with the use of a statistical software.
Both tests are considered passed if the mark is 15 or better.
The exam is passed if the average mark of the two tests is 18 or better.
In alternative, a single lab test consisting of theory and exercises questions. Students are expected to solve questions with the use of a statistical software.
The exam is considered passed if the mark is 18 or better.
Contents
1. DESCRIPTIVE STATISTICS
1. Introduction to statistical phenomena. Classification of measures. Frequency distributions (absolute, relative and cumulative frequencies). Graphical methods for representing quantitative and categorical measures.
2. Position indices: means (and properties); mode, median and percentiles.
3. Variability indices: variance, standard deviation, coefficient of variation (and properties). Box-plot.
2. PROBABILITY AND RANDOM VARIABLES
1. Random experiments, sample space and events.
2. Assigning a probability measure to the event. Axioms and rules of probability. Enumeration of sample points.
3. Independence and conditional probability. Law of total probability. Bayes' theorem.
4. Discrete and continuous probability distributions. Probability, density and distribution function. Expected value and variance.
5. Discrete Probability Distributions: Discrete Uniform, Bernoulli, Binomial, Hypergeometric, Geometric, Negative Binomial and Poisson.
6. Continuous Probability Distributions: Continuous Uniform, Normal, Exponential, Gamma.
7. Joint distributions and independent random variables. Covariance and correlation. Linear combination of random variables, expected value and variance. Central limit theorem and main applications.
3. INFERENTIAL STATISTICS
1. Population and sample. Sampling from finite populations. Random sample.
2. Point estimate: estimator and estimate. Sample mean, sample variance, sample proportion.
3. Properties of an estimator: unbiasness, efficiency and consistency. Properties of mean, variance and sample proportion.
Standard normal distribution (Z), Student's T, chi-square, Fisher's F.
Probability and quantile graphs.
4. Confidence intervals. Main cases of confidence intervals: for the mean of a normal distribution (known and unknown variance); for the variance of a normal distribution (known and unknown mean); for the difference between the means of two Normal populations (equal but unknown variance). Asymptotic confidence intervals: for the mean of any distribution (known and unknown variance); for a proportion; for the difference between two proportions.
5. statistical tests: null and alternative hypotheses, acceptance and rejection regions, p-value, first and second type errors, confidence levels, power of the test, power function.
6. One-way and two-way tests: for the mean of a normal distribution (known and unknown variance); for the variance of a normal distribution (known and unknown mean); for the difference between the means of two Normal populations (equal but unknown variance); for a proportion; for the difference between two proportions.
7. The simple linear regression model: parameter estimation, goodness of fit, significance test. Estimate of the dependent variable and forecast. Extension to the multiple regression model.