{"version":10,"randomSeed":"9131c6f9f3ed426e2198d4ac7f8f8777","graph":{"viewport":{"xmin":-12.773267286297244,"ymin":-8.853846163274849,"xmax":19.710134612928737,"ymax":11.299588395329526}},"expressions":{"list":[{"type":"text","id":"12","text":"cost from waiting sith you arrive too early"},{"type":"expression","id":"1","color":"#c74440","latex":"f\\left(x\\right)=\\ln\\left(1+e^{-x}\\right)"},{"type":"text","id":"14","text":"cost from (probabilistically) missing the start of the event"},{"type":"expression","id":"3","color":"#388c46","latex":"g\\left(x\\right)=\\frac{5}{1+e^{-x}}"},{"type":"text","id":"17","text":"centre of your arrival times"},{"type":"expression","id":"4","color":"#6042a6","latex":"m=-1.6","slider":{"playDirection":-1}},{"type":"text","id":"19","text":"actual arrival times are normally distributed, stddev, say, 1"},{"type":"expression","id":"5","color":"#000000","latex":"P\\left(x\\right)=\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{\\left(x-m\\right)^{2}}{2}}"},{"type":"text","id":"21","text":"total expected cost: minimise this by adjusting central time"},{"type":"expression","id":"8","color":"#388c46","latex":"\\int_{-99}^{99}P\\left(x\\right)\\left(f\\left(x\\right)+g\\left(x\\right)\\right)dx"}]}}