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Can you tell me what is the difference between empirical distribution and classical probability? My teacher has told me that when we take limit empirical distribution will get a constant value

$$P(A)=\lim_{N\rightarrow\infty}f(A)=\lim_{N\rightarrow \infty}\frac{N(A)}{N}= \mathrm{constant}$$

where $F(A)$ is the frequency ratio, $N(A)$ is the number of times Event $A$ is found to occur and $N$ is the number of times random experiment repeated

But classical probability will give

$$P(A)=\lim_{n\rightarrow \infty }\frac{m}{n}= 0$$

but what I know of limit is like this

$$\lim_{x\rightarrow\infty}\frac{1}{x}=0$$

Then how come empirical distribution is giving a constant instead of zero?

And last can you explain what and why we use axiomatic definition?

Advance thanks for your help... I am a newb to probability statistics

2 Answers 2