c) Let W € [0, ∞o) represent wind speed in miles per hour (mph). Assume that W has the following density function: f(w)

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C Let W 0 O Represent Wind Speed In Miles Per Hour Mph Assume That W Has The Following Density Function F W 1 (24.02 KiB) Viewed 28 times

c) Let W € [0, ∞o) represent wind speed in miles per hour (mph). Assume that W has the following density function: f(w) = 2 Awe Aw² where >> 0. i) Show that Pr(W> w) = e-Aw² (3 marks) ii) If there is a 1% chance of wind speeds greater than 120mph, what is the value of A? (2 marks) iii) A wind turbine only operates when the wind speed is between 10 mph and 60 mph. Calculate the probability that the wind turbine does not operate. Note: use A value from part (ii). (3 marks)