# intro to probability

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For the sheet-metal stamping machine in a certain factory, the time between failures, X1 has a mean between the failures, of 56 hours and a variance of 16 hours. The prepair time X2, has a mean time to repair of 5 hours and a variance of 4 hours.
a) If X1 and X2 are independent , find
the expected value and the variance
of Y=X1+X2, which represents one
operation-repair cycle.
b)Would you expect an operation-repair
cycle to last more than 75 hours?Why?

Work
------------------------
a) E(Y)= E(X1+X2)= EX1+EX2= 56+5=61
V(Y)= ... = 20
b) P(Y>75) = P(X1+X2 >75) =
I'm not sure where to go from here, i thought of using complement but i just got stuck.

ans: no, P(Y>75)<=0.1653

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