建于：20231230 00:14:00 Saturday 858字 3分
Sets, Probability, Conditional, Lec1, NOTE, and ProbabilityStatics
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ProbabilityTheory
 Set Theory
 Probability Theory
 Conditional Probability and Independence
 Random Variables
 Distribution Functions
Set Theory

Countable set: it consists of countable number (finite or countably infinite) of elements. For example, the set of even numbers is countably infinite; the set of prime numbers under 10,000 is finite.

Uncountable set: it consists of uncountable number of elements. For example, the number of real numbers in any interval (a, b); the set of possible outcomes from measuring human weight or height.
Probability Theory
Experiments
 Many investigations may be characterized in part by the fact that repeated experimentation.
 Each experiment terminates with an outcome.
 Suppose that we have such an experiment, the outcome of which can’t be predicted.
 If this kind of experiment can be repeated under the same conditions, it is called a random experiment.
 The collection of every possible outcome is called the experimental space or the sample space.
 Event – a set of outcomes.