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Title: Computing and Data Analysis for Environmental Applications
Description: This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.
Description: This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.
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MIT OpenCourseWare
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mit
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Brief Notes #1
Events and Their Probability
• Definitions
Experiment: a set of conditions under which some variable is observed
Outcome of an experiment: the result of the observation (a sample point)
Sample Space, S: collection of all possible outcomes (sample points) of an experiment
Event: a collection of sample points
• Operations with events
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Intersection
A
B
A
A∩B
B
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Mutual Exclusiveness - intersection of events is the null set (Ai∩Aj = ∅, for all i ≠ j)
2
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E
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∪An = S)
3
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, An} are both mutually exclusive and collectively exhaustive, they
form a partition of the sample space, S
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0 ≤ fE ≤ 1
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f(A∪B) = fA + fB if A and B are mutually exclusive
• Properties/axioms of probability
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P(S) = 1
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P(Ac) = 1 − P(A)
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, Bn} be a set of mutually exclusive and collectively exhaustive events and let A
be any other event
Title: Computing and Data Analysis for Environmental Applications
Description: This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.
Description: This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.