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. (a) What is the expected value of X? (b) What is the variance of X? (c) What is the CDF of X? (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? (g) You observe a battery who’s lifetime is in the 99th percentile. How long has this battery lasted? Show by hand and provide the appropriate R code
3. 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.
(a) What is the
(b) What is the variance of X?
(c) What is the CDF of X?
(d) What is the
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?
(g) You observe a battery who’s lifetime is in the 99th percentile. How long has this battery lasted?
Show by hand and provide the appropriate R code.
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