Download BIN0406-15 Introduction to probability and statistics (4-0-4)

BIN0406-15 Introduction to probability and statistics (4-0-4)
General goals:
The main goal of this course is to introduce the essential concepts of the theory of probability,
such as probability spaces, random variables, distribution functions, etc., together with its
implications and applications in statistics.
Specific goals:
1.
To gain the ability of solving simple counting problems.
2.
To gain the ability of solving simple probability problems.
3.
Understand the concept of a random variable and compute the probabilities of
probabilistic experiments following binomial, Poisson, normal and exponential distributions.
4.
Understand the central limit theorem and be able to use it in applications in statistics,
such as in the construction of confidence intervals.
5.
Acquire basic concepts in statistics in order to analyze and interprete experimental
data sets.
Be able to interpret measurements of position and dispersion in experimental data sets.
Syllabus:
Basic principles of combinatorics. Definition of probability. Conditional probability and
independence. Random variables. Discrete and continuous probability distribution functions.
Most important distributions: Bernoulli, binomial, Poisson, geometric, uniform, exponential
and normal. Independent random variables. Expectation value and variance. Descriptive
statistics: estimators of position and dispersion. Weak law of large numbers. Central limit
theorem.
Program:
Week 1: Basic principles of combinatorics. The principles of addition and multiplication.
Permutations, arrangements and combinations.
Week 2: Basic principles of combinatorics 2: binomial and multinomial theorems. Exercises in
combinatorics.
Week 3: Random experiments. Definition of sample space and probability. Properties of
probabilities.
Week 4: Conditional probability and independence: multiplication theorem and total
probability theorem. Bayes’s theorem and its consequences.
Week 5: Random variables. Distribution functions. Models of discrete distributions.
Week 6: Models of continuous distributions. Random vectors in two dimensions. Distribution
functions for random vectors. Exam.
Week 7: Independent random variables. Functions of random variables. Two dimensional
models.
Week 8: Expectation values; variance and covariance. Chebyshev and Markov inequalities.
Weak law of large numbers.
Week 9: Descriptive measures of frequency distributions. Position measures: mean, median,
modes and quartiles. Measures of dispersion: variance, standard deviation.
Week 10: Measures of dependence between random variables: correlation.
Week 11: Central limit theorem.
Week 12: Central limit theorem (continued). Exam.
Grading:
The professors assigned to this course, together with the course coordinator, will define the
grading criteria based on the evaluation system of the pedagogical project.
Pedagogical strategies:
The professors assigned to this course will, together with the course coordinator, define the
best pedagogical strategies for the course.
Prerequisites:
BCN0407-15 - Functions of a single variable.
Required texts:



S. Ross, A first course in probability. Pearson (2012).
V. K. Rohatgi, A. K. Md. Ehsanes Saleh, An introduction to probability and statistics. Wiley
(2001).
L. J. Stephens, Schaum’s Outlines of Beginning Statistics. MacGraw-Hill (2006).
Additional texts:
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

M. H. DeGroot and M. J. Schervish, Probability and statistics. Pearson (2011).
R. B. Ash, Basic probability theory. Dover (2008).
M. G. Bulmer, Principles of statistics. Dover (1979).