Let X be a random variable which represents the lifetime in years of a particular battery. We are given that X has an exponential distribution with rate λ = .15. (d) What is the probability that the battery fails between the fifth and sixth year? Show by hand and provide the appropriate R code. (e) What is the probability that the battery is still working after three years? Show by hand and provide the appropriate R code. (f) What is the probability that the battery is still working after five years, given that the battery is still working after two years?

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