4. (Causal inference) Consider the following causal model containing random variables LIKE TO READ, READ To, BOOKS, TESTS), with dom(TESTS) {high, low), dom(BOOKS) (many, few), and all other variables having domain true, false) Parents who LIKE TO READ are more likely to READ TO their children. Parents who LIKE TO READ are also more likely to have lots of BOOKS in their house. Both being READ TO and having lots of BooKs in the house have a causal influence on a child's performance on reading TESTS. (a) [10 points] Draw a directed graph representing the causal model Draw a directed graplh (b) 5 points List all of the back-door paths between having BOOKs in the house and performance on reading TESTs. (i.e., X-BoOKS and Y TESTS) (c) [5 points] Suppose that only the variables BOOKS, TESTS) are observable. Is the causal identifiable? Justify your