I need your help with this problem. Please help me by answering and showing explanations.

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 633' 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 (d What is the probability that both motors fail in the next 2000 hours