# A system contains two components X, Y which both need to work in order for the...

###### Question:

A system contains two components X, Y which both need to work in order for the system to run. The lifetime of component X is an exponential random variable X with parameter 2, and the lifetime of component Y is an exponential random variable Y with parameter 1. Assume that X,Y are independent. Let Z denote the lifetime of the system, which depends on X, Y

a. Describe Z as a function of X, Y

b. Find the PDF of Z

c.Find E[Z]

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