Spread of a lightbulb's lifetime

Question

A lightbulb's lifetime is exponential with a mean of 800 hours. What are the mean and variance of the bulb's lifetime?

Accepted Answer

For an exponential, the rate is \lambda = 1/	ext{mean}, so here \lambda = 1/800 per hour. The two moments are: - Mean = 1/\lambda = 800 hours (given). - Variance = 1/\lambda^2 = (	ext{mean})^2 = 800^2 = 640000 hours-squared. Because variance is the mean squared, the standard deviation is \sqrt{640000} = 800 hours, equal to the mean. Exponential lifetimes are highly variable: plenty of bulbs die young while a few last far beyond 800 hours. Takeaway. An exponential's variance is the square of its mean, so a mean-800 lifetime has variance 640000 and standard deviation 800.

Spread of a lightbulb's lifetime

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