Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

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 ...

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

In this lesson, you'll look at a way to represent discrete distributions - the probability mass function (PMF), which maps from each value to its probability. A probability mass function (PMF), ...

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 ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. Suppose the probability density function for the length of time it takes a ...

Discover how probability distribution methods can help predict stock market returns and improve investment decisions. Learn ...