A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

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 ...

In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...

The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

Stop-loss and limited loss random variables are two important transforms of a loss random variable and appear in many modeling problems in insurance, finance, and other fields. Risk levels of a loss ...

This course is compulsory on the BSc in Actuarial Science, BSc in Actuarial Science (with a Placement Year), BSc in Financial Mathematics and Statistics and BSc in Mathematics, Statistics and Business ...