# 2008 BasicProbabilityTheory AME598

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- (Qian, 2008) ⇒ Gang Qian. (2008).
*Basic Probability Theory.*Lecture Notes: AME 598 Sensor Fusion, Arizona State University, Fall 2008.

**Subject Headings:** Probability Theory, Course.

## Notes

- External Reference to: Certain Event, Continuous Sample Space, Countable Sample Space, Event Space, Guaranteed Event, Impossible Event, Probability Space, Random Experiment, Random Experiment Event, Random Experiment Possible Outcome, Random Experiment Sample Space, Random Experiment Trial Outcome, Random Variable.

## Quotes

A random variable X is a function that assigns a real number, X(ζ), to each outcome ζ in the sample space of a random experiment. … Let S_{X} be the set of the sample space. … X(ζ) can be considered as a new random experiment with outcomes X(ζ) as a function of ζ, the outcome of the original experiment.

Sample Space (S): defined as the set of all possible outcomes from a random experiment.

- Countable or discrete sample space, one-to-one correspondence between outcomes and integers.
- Uncountable or continuous sample space

A random experiment is an experiment in which the outcome varies in a unpredictable fashion when the experiment is repeated under the same condition. … A random experiment is specified by stating an experimental procedure and a set of one or more measurements or observations. … Examples:

- E1: Toss a coin three times and note the sides facing up (heads or tail)
- E2: Pick a number at random between zero and one.
- E3: Poses done by a rookie dancer,