Problem 3 (20 pts): A component has time to first failure, T, that follows a Weibull distribution with =0.5 and =10 years (based on MS-Excel's definition). Recall: In reliability theory, the reliability function of this component is defined as R(t)=1-F_T (t)

What is the probability that a given component survives 5 years without failure?

What is the expected time to failure of a given component? This is known as mean time to failure (MTTF).

A system consists of three (3) such components, all of which must work independently together for the successful operation of the system. What is the MTTF of the system?