Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
According to the Central Limit Theorem, the distribution of averages of many trials is always normal, even if the distribution of each trial is not.
Conditional probability determines the likelihood of events that are not independent of one another.
The notion of expected value, or expectation, codifies the "average behavior" of a random event and is a key concept in the application of probability.
The Galton board is a model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
The Law of Large Numbers says that when a random process, such as dropping marbles through a Galton board, is repeated many times, the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.
Markov chains are a way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
Probability theory enables us to use mathematics to characterize and predict the behavior of random events. By "random" we mean "unpredictable" in the sense that in a given specific situation, our knowledge of current conditions gives us no way to say what will happen next.
The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
The standard deviation is a way to measure how far away a given individual result is from the average result.
This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock, among other things.