Q17 9 Points Consider two variables, X and Y. X has possible values 1 and 2. Y has possible values -1, 0, 1. Here is the joint distribution represented as a table of proportions. Y=1 X = 1 2/12 X = 2 2/12 Y = 0 1/12 3/12 Y = 1 1/12 3/12 Q17.1 2 Points Explain why you know that this is a proper (valid) joint distribution. Q17.2 2 Points What is the marginal probability of P(X = 1) P(Y = 0) Q17.3 2 Points What is the conditional probability that X = 1 if Y = 0? In notation: P(X = 1 | Y = 0)? Q17.4 3 Points Suppose we have a sample size of 144 units in a simple random sample with observed probabilities given by the table above. At the alpha = 0.05 level, test the null hypothesis that the events X = 1 and Y = 0 are independent against the alternative that they are dependent. In your answer, give either a test statistic and rejection region or a confidence interval and explain how that can be used to test the hypothesis. Do you accept or reject the hypothesis that the two events are independent at the 5% level?