Probability Theory
Probability Theory - Related Videos
01:49
Probability Laws
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2019
Overview The probability of inheriting a trait can be calculated using the sum and product rules. The sum rule is used to calculate the probability of mutually exclusive events. The product rule predicts the probability of multiple independent events. These probability rules determine theoretical probability—the likelihood of events occurring before they happen. Empirical probability, by contrast, is calculated based on events that have already occurred. The Sum and Product Rules Are...
06:41
Prospect Theory
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2023
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University What’s the value of a dollar? Currencies store value to facilitate trade. Implied in any economic transaction is the value of a unit of currency. But what is the subjective value of a dollar? For a long time, economists assumed the answer to this question to be, specifically, that a dollar has a value determined by the market and that the subjective value of a dollar is always that, more or less. Beginning in the early 1970s,...
01:29
Non-probability Sampling
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2024
Non-probability sampling is a technique where the likelihood of selecting any individual from the target population is neither known nor calculable. While this approach is often more cost-effective and faster than probability sampling, it can introduce selection, response, and measurement biases, limiting how well the results can be applied to a broader population. Sampling Techniques One standard method is convenience sampling, where participants are chosen based on their accessibility. For...
01:14
Probability in Statistics
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2023
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts. An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
01:17
Probability Histograms
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2025
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
FAQs
Conditional probability updates an event’s likelihood when information about another event is available. Rather than treating the original uncertainty as unchanged, the analysis reassesses the event in light of the known information. In statistics, this mechanism connects observed conditions with revised expectations and supports more informed inference when researchers must account for what is already known.
Probability distributions organize the likelihoods associated with possible values or outcomes. They provide the basis for calculating expected values and measures of variability, allowing statistical analyses to describe anticipated results alongside the extent of random variation. This distinction helps researchers evaluate whether an observed pattern reflects meaningful structure rather than chance fluctuation.
The sample space identifies the possible outcomes included in an analysis, while additivity provides a rule for combining probabilities across events. Keeping these elements consistent helps ensure that likelihoods refer to the intended set of possibilities. In statistical work, that foundation supports probability distributions and the later estimation, testing, or prediction built from them.
A practical workflow begins by specifying the relevant sample space and assigning probabilities according to the governing rules. Researchers can then account for available information through conditional probability, organize outcomes with probability distributions, and calculate expected values or variability. These results provide a mathematical basis for statistical estimation, hypothesis testing, risk assessment, or predictive modeling.
Probability theory supplies the framework for representing random variation, which statistical estimation and hypothesis testing must distinguish from meaningful patterns. Probability distributions, expected values, and variability give researchers structured ways to describe possible outcomes and assess uncertainty. This foundation allows statistical conclusions to be connected to explicit assumptions about chance rather than treated as unexplained observations.
Probability theory supports risk assessment and predictive modeling as well as statistical estimation and hypothesis testing. Its applications extend across biology, medicine, engineering, and the social sciences, where researchers encounter uncertain outcomes and variable measurements. In these settings, the framework helps organize possible results, quantify uncertainty, and interpret patterns while accounting for random variation.