Question

Why we need multi-variate random variables and give real-life correlaated multi-variate random variable?

Answer 1

In statistics, we create models to understand the behavior of independent variables. The value or outcome of these variables could be a result of different variables. If these variables are independent, we have just two univariate distributions. However, if they are not we need multivariate distributions to understand correlation between the variables.

For instance, consider a health researcher trying to predict the life expectancy in a population using their weight and blood pressure levels. These random variables could be correlated.