For the following problems indicate true or false. Please
justify your answer. You may use examples to illustrate your
answers.
a. (2 points) For events A and B for which P(A)>0 and P(B)>0,
P(A|B) is always larger than P(A and B).
b. (2 points) If two random variables X and Y are independent, then
the coefficient of correlation between them is 0.
c. (2 points) P(A or B) > P(A) + P(B).
d. (2 points) Mean and median of a distribution are equal only when
the distribution is symmetric and uni-modal.
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