A population consists of 100,000 registered voters, of which 52% identify as a woman. Among those who identify as a woman, exactly 55% will vote for Candidate A. Among those who do not identify as a woman, exactly 45% will vote for Candidate A. A poll is taken with 300 calls. The poll is equally likely sampling with replacement. Let X = 1, if a woman is called, 0, if not a woman. Let Y = 1, if vote for Candidate A, 0, if not Candidate A. a) Determine the joint probability distribution of (X, Y ) (possible realizations of the pair and their probabilities - please do not round). b) Calculate Cov[X, Y ]. c) Calculate the (marginal) probability P(Y = 1). d) Calculate E[Y ]. e) Calculate SD[Y ]. f ) Let Y denote the sample mean (for the votes) for the 300 calls. Calculate E[Y ]. g) Calculate SD[Y ]. h) Determine the 95% probability mass interval for Y .