Question 1:

\fSuppose the data is generated following the causal graph below. In a causal graph, if there is an edge from A to B, then variable A has an direct effect on variable B. A Causal Graph. In this graph, each node is a random variable, and an edge from A to B means the variable A has direct effect on B. Recall that a confounder is a variable that influences both the dependent variable and independent variable. We are interested in the effect of X on Y. Which of the variable in the following causal graph is a confounder for variable X and Y? (Choose all that apply.) Consider an application of the Bernoulli model to the mammography study, and index the patients in the control group from 1 to 31000. Define X1, . . . , X31000 to be random variables where X,- is an indicator variable for whether patient 1' died of breast cancer. '.'.d . , . Suppose that our model for breast cancer deaths is as follows: X1, . . . ,X31000 13v Bernoulli(p). Which of the followmg statements correctly describes the model? 0 In the model's data generating process, each participant has a probability p of dying from breast cancer and each participant's death is independent from other participants 0 Of the 31000 participants, 3100019 are observed to die from breast cancer 0 Of the 31000 participants, a fixed set of 31000}? patients have a probability of 1 of dying from breast cancer and while another set of 31000 (1 p) patients have a probability of 0 of dying from breast cancer. Which of the following correctly describes the formula for the pvalue in the mammography study, given an observation of Y : 39 deaths due to breast cancer in the treatment group of 31000? O PH0 (T g 39), the probability under H0 to obtain the observed value or a more extreme value of the test statistic O PH0 (T = 39), the probability under H0 to obtain the observed value of the test statistic O PHA (T = 39), the probability under HA to obtain the observed value of the test statistic O PT