View Full Version : Help w/ P(X1+X2 >75) when only mean and variance are given.

04-20-2008, 08:39 PM
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?

My Work
a) E(Y)= E(X1+X2)= EX1+EX2= 56+5=61
V(Y)= V(X1+X2)= VX1+VX2 =16+4 = 20
got ans correct.
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 in back of book: no, P(Y>75)<=0.1653

04-21-2008, 08:51 AM
Try Chebychev's inequality.