The life x (in years) of electronic components obeys the exponential distribution with mathematical expectation of 2, and the life of each component is independent of each other. Taking 100 parts at random, the probability that the sum of life of these 100 parts is greater than 180 is as follows:

Exponential distribution is different from distributed exponential family, which is a large class of probability distribution including exponential distribution as one of its members, including normal distribution, binomial distribution, gamma distribution, Poisson distribution and so on.

Extended data:

Exponential distribution is widely used. In Japanese industrial standards and American military standards, the sampling scheme of semiconductor devices adopts exponential distribution. Exponential distribution is also used to describe the fault distribution of mean time between failure MTBF in large complex systems (such as computers).

Because the exponential distribution is characterized by a lack of "memory". Therefore, its application in the study of mechanical reliability is limited. Mechanical reliability refers to that a product or part, after working for a period of time t0, is still like a new product, which does not affect the future working life value.