1. {20 points) True/False Indicate whether each statement below is true or false, and briey explain your answer. You may refer to formulas and denitions covered in class, or use examples to illustrate your point. Each question is worth 4 points: 2 for True/ False and 2 for the justication. (a) In the one-sample case, the standard error of the sample mean increases as the sample size increases. (b) A correlation of r = 0 means that the two variables y and a: are uncorrelated. (e) Let X be normally distributed with mean 3 and standard deviation 1. The probability that X is greater than its mean is 0.5, that is P(X > 3) = 0.5. (d) If A and B are such that P(A) 76 0 and P(B) # 0 but they are mutually exclusive, then A and B are also independent. (e) Chebyshev's rule can only be applied to non-symmetrical data