= Twenty percent of iPhones are produced in Factory 1, fifty percent are produced in Factory 2, and thirty percent are produced in Factory 3. The lifetime of every iPhone made has an exponential distribution, but the mean lifetimes are different for the iPhones produced at the different factories; those produced at Factory 1 have an average lifetime of two years (the exponential parameter is ₁ = ½), those produced at Factory 2 have an average lifetime of four years (12) =), and those produced at Factory 3 have an average lifetime of five years (3) 3). You can assume that these phones work perfectly until they instantaneously stop working, at which point their lifetime is over. I do not know which factory my iPhone came from, but it is still working well after three years. Given all of this information, what is the expected value of the remaining lifetime of my phone? (5 points) =