Two discrete random variables X and Y have support sets I : {0.1} and J? : {[111}. respectively. The values of the joint probability mass function {pmf} pxrylxy] describing X. and Y are given by the following table: III[W 26116} 62 0 where it is assumed that 5 E R, J # and :5 % 1. a Discuss what is the valid range of 5. {5 marks} } b} Marginalise the joint pmf to obtain the pmf's of X and Y. [5 marks}r c) Discuss whether X and Y are independent random variables or not. [5 marks} ) d Can thejoint entropy H{X1 Y) equal the sum ofthe entropies ofX and Y {i.e., H(X] and H(Y}? Explain why. or why not, solely in terms of: your result in c}. the chain rule of entropy and the conditional entropy inequality. {5 merits}I e) Find the value of 6 that maximises the entropy of X. H(X), and then find the value of :5 that maximises the entropy of Y, H[Y}. [5 marks}