# Statistics and Probability, 6 credits (TNIU66)

Statistik och sannolikhetslära, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

### Examiner

Michael Hörnquist

### Director of studies or equivalent

George Baravdish
Course offered for Semester Period Timetable module Language Campus VOF
6IBYG Civil Engineering, B Sc in Engineering 2 (Spring 2017) 1 4 Swedish Norrköping v
6KFTL Air Transportation and Logistics, Bachelor's Programme 2 (Spring 2017) 1 4 Swedish Norrköping o
6KLOG Civic Logistics, Bachelor´s Programme 2 (Spring 2017) 1 4 Swedish Norrköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Civil Engineering, B Sc in Engineering
• Air Transportation and Logistics, Bachelor's Programme
• Civic Logistics, Bachelor´s Programme

### Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

### Prerequisites

A first course in mathematics at university level.

### Intended learning outcomes

The course aims to provide an introduction to mathematical modeling of random trials and to statistical methods and concepts. It shall also demonstrate applications relevant to the programs for which it is given. After the course the student will be able to:

• analyze the distribution of a dataset for the central value and dispersion, such as mean, median and standard deviation, and visualize this.
• describe different approaches to the concept of probability.
• calculate probabilities of events, using concepts and tools such as independence, conditioning, incompatibility, complement event, union, intersection, combinatorics, tree diagram.
• formulate a probabilistic model using random variables, also with the central limit theorem, and use it to determine the characteristics of its distribution and calculate probabilities.
• calculate point estimates of expected value, variance , standard deviation, probability and intensity, and assess their suitability.
• calculate confidence intervals for the expected value (with and without a known standard deviation), probability and intensity, and interpret the results.
• formulate and implement hypothesis testing, and therein interpret the concepts of strength functions and P-value.
• conduct a correlation analysis and interpret the results.
• set up and interpret a linear regression model with two variables, determine whether a linear model is applicable and assess the reliability of estimates of both expected values ​​as well as of individual observations.
• use computer support for all calculations where relevant.
• ### Course content

• Probability: the concepts of probability. Sample space and event. Set theory and combinatorics. Conditional probabilities, Bayes' Theorem and the concept of independent events. Discrete and continuous random variables with distribution measures such as expected value, variance / standard deviation, covariance and correlation. The most common probability models, including uniform, binomial, poisson, exponential and normal distribution model. The Central Limit Theorem.
• Statistics: Descriptive statistics with the concepts of mean, median and standard deviation, and visualizations. Point and interval estimates of the expected value (with and without a known standard deviation), probability and intensity. Point estimation of variance and standard deviation. Hypothesis testing, including P-value and intensity function. Correlation. Linear regression for two variables, including control of suitablitity and determination of confidence and prediction intervals.

### Teaching and working methods

Teaching is done in lectures, problem classes and laboratory work.

### Examination

 UPG1 Optional assignments for bonus on final exam U, G 0 credits LAB1 Laboratory work U, G 1.5 credits TEN1 Written examination U, 3, 4, 5 4.5 credits

Bonus on final exam from assignments is valid for one year.

### Grades

Four-grade scale, LiU, U, 3, 4, 5

### Other information

 Supplementary courses: Courses in simulation, quantitative logistics etc.

### Department

Institutionen för teknik och naturvetenskap

### Director of Studies or equivalent

George Baravdish

### Examiner

Michael Hörnquist

### Education components

Preliminary scheduled hours: 42 h
Recommended self-study hours: 118 h

### Course literature

Gunnar G. Lövås, Statistik - metoder och tillämpningar, Liber AB, Malmö, 2006.
Gunnar G. Lövås, Statistik - metoder och tillämpningar, Liber AB, Malmö, 2006.

### Download

 UPG1 Optional assignments for bonus on final exam U, G 0 credits LAB1 Laboratory work U, G 1.5 credits TEN1 Written examination U, 3, 4, 5 4.5 credits

Bonus on final exam from assignments is valid for one year.

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LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

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