1.Let X be a discrete random variable.You are told the following facts about the conditional probability of X given Z: for all x,

Pr(X = x | Z=0) = Pr(X = x | Z=1)

What does this tell you about the relationship between X and Z?

• A.X and Z are independent
• B.X and Z are dependent
• C.There is not enough information to determine if X and Z are dependent or independent
• D.X and Z are mutually exclusive

2.Let X be a discrete random variable.Let Z be a dichotomous random variable that only takes values 0 or 1.You are told the following facts about the conditional probability of X given Z: for all x, Pr(X = x | Z=0) = Pr(X = x | Z=1)

What does this tell you about the relationship between X and Z?

• A.X and Z are independent
• B.X and Z are dependent
• C.Not enough information to determine if X and Z are dependent or independent
• D.X and Z are mutually exclusive

3.The graph below (if you have trouble viewing the plot you have the option of downloading the attached doc file) plots pre-test (x-axis) versus post-test (y-axis) scores for both treatment observations (red dots) and control observations (blue dots); the associated regression lines for treatment and control groups are overlaid.Let Y denote post-test score.Let X denote pre-test score.Let Z denote treatment versus control.Which of the following statements are supported by this plot (check all that apply).

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