Question
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.)
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