Probability, Statistics and Computer Science

MODULE 1: Probability and Statistics.

Descriptive statistics:
1)Sampling from populations. Types of data and variables.
2)Partitioning of data into classes and construction of frequency tables. Histograms and bar charts.
3)Centrality indexes (mean, mode, median, midrange). Dispersion indices (range, standard deviation, variance), percentiles, quartiles. Outliers, boxplots.
Probability and random variables:
4)Sample space, events, probability of events
5)Probability of union and intersection of events. Complementary events. Independent events. Conditional probability. Bayes theorem. Factorials and binomial coefficients.
6)Random variables. Expected value, variance and standard deviation of discrete r.v.
7)Discrete r.v.'s: binomial and Poisson. Continuous r.v.'s: uniform and normal.
8)Standardization and properties of normal distribution. Normal approximation of the binomial distribution.
Inferential statistics:
9)Fundamental concepts: population, sample, parameter, statistics, estimator. Behaviour of the sample mean: law of large numbers and central limit theorem. Punctual estimate.
10)Confidence intervals: general concepts. Confidence interval for a proportion.
11)Confidence interval for the mean, both with known and unknown standard deviation. T Student distribution.
12)Statistical hypothesis testing. General concepts: null and alternate hypotheses, first and second type errors, significance level, power function, p value, test statistics, critical region.
13)Hypothesis test on a proportion. Hypothesis tests on the mean (both with known and unknown variance)
14)Inference for two samples: inference for two proportions. Inference for two means, both for paired or independent samples.
15)One and two way ANOVA

Bivariate statistics:
16)Test of independence and of fit. Chi squared distribution.

Computer lab
17)Illustrative examples of applications of descriptive, inferential and predictive statistics on real data, through the use of simple statistical softwares.

MODULE 2: Informatics

The module consists of theoretical lectures and labs.
Theory:
1) The meaning of Computer Science, algorithms and programs;
2) Computer architecture and digital information;
3) Low and high level programming: compilers and interpreters;
4) Foundations of structured programming;
5) The Python language: data types, control structures, functions and files.
Lab:
1) Operating systems and file system;
2) Programming environment and tools;
3) Programming activity related to theoretical topics above presented.