A data scientist is interested in studying the relationship between having a social media account and obesity. He collected some data represented in the following table. Individual Having a social media account Obesity Individuall Yes Individual2 Yes Individual3 Yes Individual4 No Individual5 Yes Yes Yes Yes No No (a) Find the probability distributions of having a social media account and being obese. (b) Find the joint probability distribution of having a social media account and being obese. (c) Are these two distributions independent? (d) The data scientist is interested in whether having a social media account helps gain in- formation about obesity. The concept of mutual information quantifies how one feature is related to another future. For two random variables X and Y, the mutual information is defined as follows. mutual information - Pxy(x,y) In zy PX,Y(x, y) PX(T)py (y)) Suppose the joint probability distribution of having a social media account and obesity is shown by px,y(x, y) and the marginal distributions of having a social media account and obesity are px (r) and py(y) respectively. Compute the mutual information between having a social media account and obesity. [You can use a calculator to find In(z).] (e) Theoretically, what is the mutual information of two independent random variables?