A small commercial passenger aircraft has fuel efficiency that varies under different conditions. One factor is the weight of the aircraft when it takes off, including fuel, crew, cargo, and any passengers. Suppose that this take-off weight in metric tonnes is modelled by a continuous random variable W with normal distribution N (38, 4). (a) Calculate the probability that an aircraft at take-off has weight between 35 and 40 tonnes. [2 points] (b) Calculate P(W > 42). [1 point] Over time it is observed that in regular use the fuel efficiency X, measured in miles per UK gallon (mpg) is distributed with the following PDF and CDF. fx(a) = 4(x - x3) 0521 otherwise 0 Fx(2) = 272 (c) Calculate the expected value of X. [1 point] (d) Calculate the probability that fuel efficiency is between 0.5 and 0.75 miles per gallon. [1 point] Random variable Y is an approximate measure of fuel efficiency using the alternate metric unit of litres of fuel per kilometre. Y - 2V2 X