Question: 2 (Probability Distributions, Distribution Parameters) A machine in the production line has a mean lifetime (i.e. time until replacement or upgrades) of 15 years, and

2 (Probability Distributions, Distribution Parameters) A machine in the production line has a mean lifetime (i.e. time until replacement or upgrades) of 15 years, and its lifetime is distributed according to the following probability density function (pdf): f(t) = 0.006(t2 30t + 200), 10 < t < 20, 0, otherwise. a) Find the cumulative distribution function F(t) for this distribution. (2 marks) b) Hence, or otherwise, calculate the probability that the machine's lifetime will exceed 18 years. (1 mark)

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