What are the key concepts in advanced probability theory?

What are the key concepts in advanced probability theory?

Key concepts include random variables, probability distributions, expectation, variance, and the law of large numbers.

Can you explain the law of large numbers?

Sure! The law of large numbers states that as the number of trials increases, the sample mean will converge to the expected value.

What is the difference between discrete and continuous probability distributions?

Discrete distributions deal with countable outcomes, while continuous distributions handle outcomes over a range of values.

How is the Central Limit Theorem related to probability theory?

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as sample size increases, regardless of the original distribution.

Can you give an example of a real-world application of probability theory?

Certainly! Probability theory is used in fields like finance for risk assessment, in medicine for predicting disease spread, and in machine learning for making predictions.