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Problem 2. The motor in a new building's HVAC system was just installed today. There is a replacement motor available to install when the rst one fails. Let the lifetimes of the two motors (in thousands of hours) be represented by the random variables X and Y, respectively. X and Y have the joint pdf 639 when a: and y are both positive, and 0 otherwise. (a What are the marginal distributions of X and Y? (b Are X and Y independent? (0 What is the probability that the motor you just installed fails in the next 1000 hours? J J ) ) (d What is the probability that both motors fail in the next 2000 hours