I don't know if this is correct, but it seems plausible. For the first time, Magic Keyboard brings a fullheight function key row to MacBook Pro. So the optimum should be at start = 0.0584312 with a mean residual life of 0.0418137. The new MacBook Pro is available in 14 and 16inch models. If we plot pdf2 it looks exactly as your Plot Plot, ]Īnd after some errors (your function is not defined below 0, so I guess the minimizer pokes a little in that forbidden region) we get Let's extract it from your definition above into simple functions: pdf := (1/(2*(a + b)))*a*b* NExpectation or Expectation compute the expected value.įor the expected value, we only need the PDF of your distribution. I'd suggest to try it without Mathematica magic.įirst let's see what the MeanResidualLife is, as you defined it. Since your function is quite complicated (and probably not differentiable), the second possibility is to do a numerical minimization, which requires many evaluations of your function. Finding a minimum requires either to set the first derivative of the function zero and solve for a solution. Now, the FindMinimum or similar functions try to find a minimum to the function.
As far as I see, the problem is (as you already wrote), that MeanResidualLife takes a long time to compute, even for a single evaluation.
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