Statistical divided into descriptive statistics and inferential statistics. Inferential statistics refers to make inferences about the general characteristics of the sample through data, it has three elements: 1 random sample of data observations; 2 conditions and assumptions issues; three pairs of overall made be expressed in the form of probabilities. infer. Therefore, inferential statistics and probability theory are inseparable.
Random events, basic events, sample space
Random events is probability theory is a very important concept, it does not refer to a test, but rather a test result , you can use A, B, C, etc., by an inevitable event is represented by $ \ Omega $, with $ unlikely event \ Phi $ express.
Random events referred to as an event, to pay attention to this concept refers to the results of the tests (rather than the test itself), this result can be a value, it can also be expressed in words.
The basic events are random events that can not be broken down into multiple events. In one test, although the test results have many possibilities, but the results of a test can only be a result of all of that kind of basic events can only occur. The sum of all the results of tests that all all the basic events, called the sample space , denoted by $ \ Omega $ (inevitable event).
Probability of random events
He says the results of a trial that has many possible, then all the results, the event A (may be basic events, it may be a combination of several basic events) possibility of how much? This possibility is the event A probability , denoted as $ P (A) $, it is clearly a value. There are classical definition of probability, statistical definition, the definition of subjective probability, we focus on statistical definition .
Statistical definition of probability:
Under the same conditions, randomized trial $ $ n-times, event A $ m $ times, the ratio $ m / n $ referred event A frequency ; n-$ $ with the increase of the frequency in a constant $ p $ fluctuations, stable, stable value of the frequency of occurrence of event a is the probability :
$$P(A)=\frac{m}{n}=p$$
The nature of probability
1. For any random event A, there
$ 0 \ leq P (A) \ leq 1 $
2.
$$P(\Omega )=1$$
$$ P (\ Phi) = 0 $$
3. If A and B are mutually exclusive, then
＄P(A\cup B)=P(A)+P(B)＄
Addition rule of probability
for
Conditional probability, the multiplication formula, independent events