## Abstract

A single discrete random variable is depicted by a stick diagram, a 2D picture. Naturally, to visualize a bivariate discrete distribution, one can use a bivariate stick diagram, a 3D picture. Unfortunately, many students have difficulty understanding and processing 3D pictures. Therefore, we construct an alternative 2D disc plot to depict the bivariate distribution of (X$$ X $$, Y$$ Y $$), from which we obtain graphically the conditional distributions of Y$$ Y $$ given X=a$$ X=a $$, and X$$ X $$ given Y=b$$ Y=b $$; the marginal distributions of X$$ X $$, Y$$ Y $$, X+Y$$ X+Y $$, X−Y$$ X-Y $$. Furthermore, we depict the mean and the standard deviation of each distribution using a single-headed arrow. We hope these visualizations will help students better comprehend these concepts and avoid some misconceptions.