The first step is to ensure that the given distribution actually is a valid probability distribution. As mentioned earlier, this involves checking two key properties: non-negativity and summation to ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Covariance: a measure of the direction of the linear relationship between two variables. Discrete ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...

The weak convergence of empirical distribution functions subject to random perturbations and scale factors to a Gaussian process is established. This result is used to study the efficiencies of tests ...