Problem 57A
A factory owner purchased two identical machines for her factory. Let and be the lifetimes (in years) of these two machines. These lifetimes are modeled by the following joint probability density function.
The machine whose lifetime is modeled by the random variable came online 2 years after the beginning of operation of the machine that is modeled by the random variable .
Given that exceeds 2, that is the probability that exceeds 3?
Problem 57B
A company purchased two machines for its factory. Let and be the lifetimes (in years) of these machines. The following is the joint density function of their lifetimes.
The machine whose lifetime is modeled by the random variable came online after the failure of the machine whose lifetime is modeled by .
What is the variance of the total time of operation of these two machines?
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