Basic Concepts

1. Experiment (실험)

- Any action or process by which observations (or measurements) are generated.

- The only way in which an investigator can elicit information about any phenomenon is to perform the experiments.

- Each experiment terminates with an outcome.

- If an experiment can be repeated under the same conditions, it is called a random experiment.

2. Sample space $ S $ (표본 공간 $ S $) 

- The sample space is a set that contains all possible outcomes of a particular experiment.

• The number of outcomes in the sample space can be finite or infinite.
• Infinite sample space can be countable or uncountable. A sample space is countable if the elements of the sample space can be put into 1-1 correspondence with a subset of the integers.

 

3. Event (사건)

- An event of a sample space $ S $ is a subset of $ S $ (including $ S $ itself).

• A simple event contains only one outcome. Denoted by $ w $.
• A compound event contains two or more outcomes.

Experiment	Sample Space	Events
Tossing a coin	{$H, T$}  : finite	$\emptyset$, {$H$}, {$T$}, {$H, T$}
Rolling a dice	{1, 2, 3, 4, 5, 6} : finite
Observing  the number of accidents at an intersection	{0, 1, 2, ...} : infinite - countable
Observing the survival time of a patient	{t : 0 < t} : infinite - uncountable

 

 

4. Probability (Relative Frequency Approach)

- Suppose that an experiment is performed N times.

- The relative frequency for an event A is $ A occurs \over N $  = $ f \over N $.

- If we let N get infinitely large, $$ P(A) = lim_{N\to\infty}{f_N \over N}$$

 

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