Main Question or Discussion Point
I've come across a number of problems in elementary probability theory and statistics that can be exemplified as follows:
The lifetime, in years, of a certain class of light bulbs has an exponential distribution with parameter λ = 2. What is the probability that a bulb selected at random from this class will last more than 1.5 years?
The lifetime of a particular type of fluorescent lamp is exponentially distributed with expectation 1.6 years. [...]
Naturally, real lamps decay over time, so their lifetimes can't be memoryless. With that being said, is the exponential distribution a good approximation for the statistical lifetimes of any real lamps? Why/why not? If not, are there any other macroscopic systems whose lifetimes are modeled well by the exponential distribution?Suppose that the lifetime of a particular brand of light bulbs is exponentially distributed with mean of 400 hours. [...]