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Problem 4. A task will be randomly assigned to one of three machines: to Machine A with probability 0.6, to Machine B with probability 0.3, or to Machine C with probability 0.1. You are given the following information Machine A completes the task in a random time with mean 10 hours and standard deviation 10 hours Machine B completes the task in a random time with mean 30 hours and standard deviation 20 hours Machine C completes the task in a random time with mean 50 hours and standard deviation 20 hours If T is the total time to complete the task, calculate Var(T)

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Answer #1

here E(T) =0.6*E(A)+0.3*E(B)+0.1*E(C)=0.6*10+0.3*30+0.1*50=20

therefore V(T)=0.6*Var(A)+0.3*Var(B)+0.1*Var(C)+0.6*(E(T)-E(A))2+0.3*(E(T)-E(B))2+0.1*(E(T)-E(C))2

=0.6*102+0.3*202+0.1*202+0.6*(20-10)2+0.3*(20-30)2+0.1*(20-50)2 =400

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