variance

Variance is the mean of the squared deviations from the mean, the measure of how widely the observations are dispersed around the central value.

Learn how variance and covariance describe the dispersion and relationship between random variables, with examples and clear formulas.

The Bernoulli distribution models the outcome of a single experiment that can result in only two mutually exclusive events: success or failure. The Bernoulli distribution is defined by the probability mass function:

\[
b(x;p) = p^{x}\\,(1-p)^{\\,1-x}
\]

A continuous random variable \( X \) is said to follow a uniform distribution on the interval \(A = [a, b]\) if its probability density function is constant on that interval. Formally we have:

\[
U(x;a,b) =
\begin{cases}
\dfrac{1}{\\,b – a\\,} & x \in A \\\\[0.6em]
0 & x \notin A
\end{cases}
\]