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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 it gives a result of no coal 97% of the time. However, the test also incorrectly identifies a sample as not 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 given by: f(x) 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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