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There are two fuses in an electrical device. Let X denote the lifetime of the first...

There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let Y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is

f(x,y)=12xy(1-y), 0<x<1, 0<y<1

What is the probability that both fuses last at most 6 months?
  
    What is the probability that the first fuse lasts longer than 6 months given that the second fuse lasts 3 months.
   
    Find the expected lifetime of the first fuse given that the second fuse lasts 3 months.

    Find the expected lifetime of the second fuse.

    Are X and Y independent? (Write "independent" or "not independent" here. Please explain the details on your paper.)

Math   Statistics-And-Probability   
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