Continuous random variables can take any value within a range. Unlike discrete variables, they include fractional and decimal values. These variables are often modeled using probability distributions.

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Abstract: This paper derives a new type of formula for the probability that, among a collection of items with s-independent exponential times to failure, a certain subset of them fails in a given ...

The probability density function of a uniform random variable looks like a horizontal line segment over the support. This indicates that for any interval of a given length within the support, the ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Discrete Variable: not continuous variable (cannot take on any value between two specified values).

Abstract: We introduce the domain of continuous random variables (CRV) over a domain, as an alternative to Jones and Plotkin's probabilistic power domain. While no known Cartesian-closed category is ...

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. The chi-square distribution is often used in ...

Amusement park patrons, wanting to go on a log ride, might not have to wait in line at all, they might have to wait for hours, or the wait could be anywhere in between. For a random log rider, the ...