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1) A mining company has a test that can identify coal in a sample. We know that 93% of a particular area that the mining company has leased contains no coal. Given a sample that has no coal is tested, containing coal (given it actually does contain coal) 4.5% of the time. a) State each event. b) Write out the probabilities for this scenario using the probability notation taught in lectures and workshops c) Find the probability of finding coal in a sample, given the test indicates that the sample contains coal 2) The lifetime in years of a certain type of electronic component has a probability density function givern by: 051 51 otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years

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(A)Ler c be the event tvarasannple con teot indicali contaens Coal Then c he he event hat y sample conteem no coal test inelicares et A, be Th aia that e e minining company Gas ing Bempany has ceased containy no cao : 0.0 ニo-35S P( Sample conteins coal)- PCc) = o.og475 P(Finding Ce coal ina sample iven hetest indicates that inali cales that the sample Contaen Coal) PCc) 0 0947S 0.70 sご-Tiu lifetime-c.elechronic component Ra, 더porbq abil demig feunclio 5 5 5 づ 5 5 X3 5 5. 5 0.6f

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