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

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Discrete Variable: not continuous variable (cannot take on any value between two specified values).

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 ...

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 ...

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 ...

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 ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...