3: Probability
- Page ID
- 47231
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- 3.1: Events
- Definition of events, and explanation of the difference between simple and composite events.
- 3.2: Conditional Probability
- Explanation of composite probability, and equations for describing situations involving composite probability.
- 3.3: Bayes' Rule
- Overview of Bayes' Rule and its applications in finding the probability of a simple event conditioned on a composite one, using the probability of the composite event conditioned on the simple one.
- 3.4: Random Variables
- The role of the random variable \(x\) in situations where each event in a sample space is assigned a numerical value, including in finding the mean value and variance.
- 3.5: Continuous Random Variables and the Probability Density Function
- Introduction to continuous random variables, which require the use of the probability density function to find the mean value of the random variable \(x\) and of its functions.
- 3.6: The Gaussian PDF
- Overview of the normal, or Gaussian, probability density function
- 3.7: The Cumulative Probability Function
- The Cumulative Probability Function, how it relates to the probability density function, and its role in transforming the pdf of a random variable into the pdf of a function of that random variable.
- 3.8: Central Limit Theorem
- The Central Limit Theorem as a property of random variables, and a brief overview of its real-world applications. A rather amazing property of random variables is captured in the central limit theorem; that a sum of random variables taken from distributions - even many different distributions - approaches a single Gaussian distribution as the number of samples gets large.