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

So far, you learned about discrete random variables and how to calculate or visualize their distribution functions. In this lesson, you'll learn about continuous variables and probability density ...

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 ...

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).

Density functions are nonnegative for all real numbers but greater than zero only at a finite or countably infinite number of points. Density functions are nonnegative for all real numbers and are ...

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 ...

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 ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...