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Course module: UCSCIMATL4
UCSCIMATL4
Introduction to Probability and Statistics
Course info
Course codeUCSCIMATL4
EC2.5
Course goals
 
Content
Content
Summary:  The lab will introduce the student to fundamental probability notions, illustrated through applications in statistics.  The objective is twofold: first, to introduce the students to stochastic notions and reasonings; second to compensate the illiteracy in statistics traditional in science students.  The probabilistic part will be complete, but intensive.  The statistical part will concentrate on applications of interest in scientific labs.  In particular, inference techniques related to hypothesis testing will not be discussed.  These techniques may be the object of complementary courses or seminar sessions offered within the College.  
Format
The lab will be given by researchers from the stochastics group at the Mathematics Department of the University of Utrecht, under the direction of Prof. Fernandez. 
Tentative Program:
1st part: Introduction to probability (4 days)
  • Probability spaces: Events, probability measures, probability of unions and intersection of events.  Conditional probability, Bayes formula 
  • Random variables: laws, distribution functions, discrete and continuous random variables. Expectations: mean, variance and standard deviation. 
  • Main laws: Bernoulli, geometrical, binomial, Poisson, normal, exponential.   
  • Main theorems: law of large numbers and central limit theorem.
2nd part: Introduction to statistics (4 days)
  • Introduction to R (other programs also accepted, e.g. Minitab, Excell, SAS, SPSS)
  • Basic statistical notions: Population vs sampling, measures of central tendency and dispersion. Estimators: Unbiasedness and efficiency.

    Confidence intervals: Significance, comparison tests for one and two means (normal and t-test), confidence intervals.

    Regression: Least squares and linear regression, goodness of fit.
3rd part: Special project
Tentative topics:

 
  • Markov processes
  • Poisson processes
  • Random walks
  • Bootstrap techniques
  • Maximum likelihood
  • Multiple linear regression
  • Error analysis in physical measurements
  • Applications to epidemiology
There will be a review day for students to ask questions and work on their projects.  The presentation will be done during the last day of the second week.

Attendance
Due to the short duration and intensive nature of the lab course, 100% attendance is required.
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Kies de Nederlandse taal