Q4. (25') The joint probability density function of the lifetimes X and Y of two connected components in a machine can be modeled by fx,Y (x, y) xe *(ly), x 0 and y 0 0, otherwise (a) (5') What is the probability that the lifetime X of the first component exceeds 3? (b) (5') What is the expected value of (X Y) ? (c) (8') What are the marginal probability density functions of X and Y? Are the two lifetimes independent? Explain. (d) (7') What is the probability that the lifetime of at least one component exceeds 3