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The uniform distribution explained, with examples, solved exercises and detailed proofs of important results
What is a Uniform Distribution? The uniform distribution is a symmetric probability distribution where all outcomes have an equal likelihood of occurring. All values in the distribution have a constant probability, making them uniformly distributed.
Topics discussed include uniform distribution characterization of Benford's law, uniform distribution of sequences and functions, and uniform distribution of random variables.
2 kwi 2023 · The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.
For example, for the normal distribution, (location/shape) are given by (mean/standard deviation) of the distribution. In contrast, for the uniform distribution , location/shape are given by the (start/end) of the range where the distribution is different from zero.
The distribution of Figure 12.1 is unimodal, meaning it has one distinct peak, but distributions can also be bimodal, meaning they have two distinct peaks. Figure 12.2, for example, shows a hypothetical bimodal distribution of scores on the Beck Depression Inventory.
Introduction. The characteristic function is a way to describe a random variable. The characteristic function, a function of t, determines the behavior and properties of the probability distribution of the random variable X.
