What is the definition of a bivariate probability distribution?

A bivariate probability distribution is defined as a probability distribution involving two random variables. It captures the relationship between these two variables, allowing for the evaluation of joint probabilities and the exploration of how changes in one variable may affect the other. This distribution is crucial in fields such as statistics and data analysis because it provides a framework to examine the interactions and correlations between two distinct sets of data.

In this context, the concept of joint probability is key, as it enables the calculation of probabilities concerning combinations of outcomes for the two variables. Additionally, bivariate distributions can be visualized through scatter plots or bivariate probability density functions, providing insights into the correlation and dependence between the two variables.

The other options do not reflect the essence of a bivariate probability distribution. A distribution involving a single random variable refers to univariate distributions, while displaying only discrete values pertains to discrete probability distributions, which may not capture the full range of relationships that can exist between two continuous variables. Lastly, a function that illustrates a single outcome does not align with the definition of a distribution that describes multiple outcomes for two variables.