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- A random variable X is said to be uniformly distributed over the interval -∞ < a < b < ∞.
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Apr 2, 2023 · If \(X\) has a uniform distribution where \(a < x < b\) or \(a \leq x \leq b\), then \(X\) takes on values between \(a\) and \(b\) (may include \(a\) and \(b\)). All values \(x\) are equally likely. We write \(X \sim U(a, b)\). The mean of \(X\) is \(\mu = \frac{a+b}{2}\). The standard deviation of \(X\) is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\).
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The uniform distribution is characterized as follows. A random variable having a uniform distribution is also called a uniform random variable. Sometimes, we also say that it has a rectangular distribution or that it is a rectangular random variable. To better understand the uniform distribution, you can have a look at its density plots.
This section shows the plots of the densities of some uniform random variables, in order to demonstrate how the uniform density changes by changing its parameters.
Please cite as: Taboga, Marco (2021). "Uniform distribution", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/probability-distributions/uniform-distribution.
Mar 2, 2021 · The uniform distribution is a probability distribution in which every value between an interval from a to b is equally likely to occur. If a random variable X follows a uniform distribution, then the probability that X takes on a value between x 1 and x 2 can be found by the following formula: P(x 1 < X < x 2) = (x 2 – x 1) / (b – a) where:
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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.
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 of endpoints. Example 5.2.
A continuous random variable X is said to have a Uniform distribution over the interval [a, b], shown as X ∼ Uniform(a, b), if its PDF is given by. fX(x) = {1 b−a 0 a <x <b x <a or x> b. We have already found the CDF and the expected value of the uniform distribution.
A random variable X has a uniform distribution on interval [a, b], write X ∼ uniform[a, b], if it has pdf given by. f(x) = {1 b − a, for a ≤ x ≤ b 0, otherwise. The uniform distribution is also sometimes referred to as the box distribution, since the graph of its pdf looks like a box. See Figure 1 below.
