The range of correlation coefficient of any bivariate discrete random vector with finite or countably infinite values is derived. We show analytically that the normal-transformed discrete bivariate ...

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

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 ...