1. In this example, you need to provide an example of a joint probability mass function or joint probability density function that satisfies certain conditions.

(a)  Construct an example of a pair of discrete random variables which have Corr(X, Y) = 0.1. It means you should provide a joint probability mass function (PMF) of X and Y. Show that Corr(X, Y) = 0.1 in your example.

(b)  Construct an example of a pair of continuous random variables which have Corr(X, Y) = 0.1. It means you should provide a joint probability density function (PDF) of X and Y. Show that Corr(X, Y) = 0.1 in your example.