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(Solved): t, in hours\mu _(A)^(*)(t)=ln((12)/(9)),t>0 \mu _(z)0dots\mu _(Z)(t)=0.001,t>0dotsAB$500,0000% ...
t, in hours\mu _(A)^(*)(t)=ln((12)/(9)),t>0
\mu _(z)0dots\mu _(Z)(t)=0.001,t>0dotsAB$500,0000%\mu _(B)^(*)(t)=(1)/(9-t),0
a. Assuming the common-shock failure rate, \mu _(z), is 0dots
i. Calculate the probability at least one engine is still running at the end of a 6-
hour trans-Atlantic flight.
ii. Calculate the probability neither engine is still running at the end of a 6-hour
trans-Atlantic flight (as if you didn't know that was coming).
b. Trans-Atlantic flights are not without other perils (e.g., storms, terrorism, sparrows).
Assuming the common-shock failure rate \mu _(Z)(t)=0.001,t>0dots
i. Calculate the probability at least one engine is still running at the end of a 6-
hour trans-Atlantic flight.
ii. Calculate the probability neither engine is still running at the end of a 6-hour
trans-Atlantic flight (as if you didn't know that was coming again).
iii. Calculate the probability that engine A is running, but engine B is not.
iv. Calculate the net single premium of an insurance product that pays $500,000 in
the event of a plane crash due to both engines failing. Assume the discount rate
is 0%.