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4. Jane and Sally make phone calls whose lengths are independent and identically distributed exponential random...

4. Jane and Sally make phone calls whose lengths are independent and identically distributed exponential random variables with mean 3 minutes. Assuming the calls begin at the same time, what is the expected time until both are completed?

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Answer #1

here let parameter of 1st and 2nd phone calls are 1 and 2

from above 1 =2 =1/3

therefore expected time until both are completed =1/1+1/2-1/(1+2) =1/(1/3)+1/(1/3)-1/(3+3) =3+3-3/2 =4.5 minutes

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