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Facoltā di Scienze Agrarie e Alimentari Universitā degli Studi di Milano
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Mathematics and Statistics turn 2
Code: G280PB
Teacher:  Paola Morando
CFU subdivision: Lectures: 3
Practices in classroom: 1
Basic aims:  Knowledge of the basics of Maths, in particular, of elementary
Calculus (real functions in one variable, limits, derivatives,
integrals).Knowledge of descriptive statistics. Knowledge of the
position and variability indicators. Knowledge of methods of
inferential statistics. Acquisition of the principles and techniques of
regression and correlation between various parameters.
Acquired skills:  Possibility of exploiting the basic tools of Maths in any context.
Describe the phenomena by the main statistical indicators; plan
sample surveys; use the methodology of the analysis of variance
at 1 and 2 factors; understand the results of statistical surveys.
Course contents:  Data analysis and description
Discrete probability distributions
Continuous probability distributions
Sampling and sampling distributions
Testing hypotheses
Program:  Data analysis and description
The language of Statistics, Frequency distributions, Graphical
representation of statistical data, Dispersion and correlation
graphs, Minimal square method, Incorrect and misleading
graphic representations, Central trend indices and dispersion
indices, Position and outlier measures, Shape of a distribution.

Random (or casual) experiments, sample space, events, The
concept of probability
Combinatorial probabilities, Conditional probability, Total
probability theorem and Bayes theorem, Sensitivity, specificity
and predictive value of a test

Random variables and probability distributions
Random variables, Continuous and discrete probability
distributions, Parameters of a distribution

Discrete probability distributions
Binomial or Bernoulli distribution, Media and variance of a
binomial distribution, Using binomial distribution tables,
Graphic representation of the binomial distribution

Continuous probability distributions
Normal or Gauss distribution, Standardized normal distribution
and its applications, Relationship between binomial distribution
and normal distribution

Sampling and sampling distributions
Populations and samples, Average sampling distribution,
Central limit theorem, Estimating the parameters, Unilateral
and bilateral confidence intervals, Student distribution t

Testing hypotheses
General concepts, Choice of hypotheses, Significance level,
Type I and II errors, Test of bilateral and unilateral hypotheses,
Test of population hypothesis, Standard Deviation known,
Standard deviation unknown, Test of the chi-squared
Prerequisites:  nothing
Preparatory instructions:  nothing
Learning materials:  Fondamenti di statistica. Con aggiornamento online, Michael III
Sullivan Curatore: E. Zavarrone
EAN: 9788865189450
Other info:  Only students which are regularly registered using SIFA will be
admitted to the exam.
The final examination consists of a written and an oral part.
Both of them are mandatory. Only students who have been
approved (with a mark of at least 18/30) in the written
examination will be admitted to the oral part.
The written examination is designed to test computational
skills, while during the oral part the theoretical understanding
of the different topics discussed during the course will be
The written examination is organized in three parts: the first
one, called Part A, lasts 30 minutes and is composed by 10
open questions about basic mathematics. The questions,
extremely simple, aim at evaluating if the student possesses
the minimal requirements to approach a university math’s
The Part A is passed if the student answer correctly to at least
8 question (over 10). Passing Part A is a necessary (but not
sufficient!) condition to pass the written examination. The
second part, or Part B, will last 1.30 hours and will be make of
open exercises about math topics, while the third and last part,
Part C, will consist in open questions about statistics.
The written examination will be passed if all of the three parts
will be passed: the first one with at least 8 over 10, the second
one (Maths) with at least 11 over 18, and the last part
(Statistic) with at least 7 over 12. The final score will be
obtained adding the scores of Maths (part B) and Statistics
(part C). The score of the first part (if passed) does not
contribute to the final score of the written examination.
During the first two parts (Part A and Part B) the use of
calculator is not allowed, while a non-programmable calculator
can be used in the third part.
Program of Mathematics and Statistics turn 2 (pdf version)
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