I need solving 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) he represented by the random variables X and Y, respectively. X and Y have the joint pdf 8":'9 when :1: and y are both positive, and 0 otherwise. (a) What are the marginal distributions of X and Y? (b) Are X and Y independent? (c) What is the probability that the motor you just installed fails in the next 1000 hours? ((1) What is the probability that both motors fail in the next 2000 hours