Question

Suppose that a die-hardly-ever battery has an exponential time-to-failure distribution with a mean of 48 months. at 60 months, the battery is still operating. what is the probability that the battery is going to last for the next 12 months?

Answer 1

Since the time to failure distribution is exponential, the distribution is F (n) = 1 – e ^ (-x/48)

The probability of failure between months 60 and 72 is the same as the probability that the battery will fail in 12 months, since the exponential distribution is memoryless F (12) = 0.221