1. Randomized test
Experiment: Make an observation or conduct a scientific experiment on a phenomenon.
Features:
(1) can be repeated under the same conditions.
(2) The possible results of the test are more than once, but all possible results can be known before the test.
(3) It cannot be determined which result will appear before the test.
2. Sample space
For a random experiment E, the set of all possible outcomes of E is called the sample space of E, denoted as S. where an element in S, that is, each possible outcome of E, is called a sample point.
3. Events
Generally, we call a subset of the sample space S of experiment E a random event of E, or event for short. Generally represented by capital letters A, B, C...
A single point set consisting of a sample point is called a base event.
In each trial, an event is said to occur when one of the sample points in the event occurs.
Inevitable event: An event that must occur in each trial.
Impossible event: An event that must not occur in each trial, denoted by Ø.
Fourth, the event relationship
Include
and events
accumulated events
Difference case
mutually exclusive events
inverse event
5. The law of event operation
commutative law
associativity
distribution rate
De Morgan's Law
6. Frequency
Under the same conditions, repeat n trials, the number of times event A occurs n A trials is called the frequency of occurrence of A, and n A /n is called the frequency of event occurrence.
7. Probability
When the number of repetitions n of the experiment increases gradually, the frequency of event A will gradually stabilize at a constant p. This p is the probability that event A occurs, which is used to indicate the possibility of event A occurring in a trial, and the probability of event A is recorded as P(A).
The conditions that the probability needs to meet:
(1) Non-negativity: P(A) ≥ 0
(2) Normative: For an inevitable event S, there is P(S)=1
(3) Listable additivity
8. Geometric outline
For test E, if:
(1) The sample space of the experiment contains an infinite number of elements
(2) The probability of occurrence of each basic event in the experiment is the same, that is, the probability of occurrence of each basic event is equal
Such an experiment E is called a geometrical profile, where P(A) = the length of the region (area or volume) that makes up event A/the length of the region (area or volume) that constitutes the total results of the experiment.