The exponential distribution is a simple distribution that is often used to calculate engineering reliability. In mathematics, it is used in case of improper use. It is used to form the behavior of a unit with a stable failure rate. The exponential distribution is a continuous probability distribution function, which can be the probability density function of the exponential distribution from the following formula (pdf).

\(f(x,λ)=λe^{-λx}\)

Where x is a random variable and λ is a distribution parameter

In the reliability study of electronic components, it is usually used to describe the measurement results of the number of defects or system failures that occur. This distribution shows that the smaller the mean, the more the distribution is skewed.

Exponential distribution is widely used.In the Japanese industrial standards and the US military standards, the sampling schemes of semiconductor devices are all exponentially distributed. In addition, the exponential distribution is also used to describe the failure distribution of the mean time-of-failure MTBF of large complex systems such as computers. However, due to the lack of "memory" characteristics of the exponential distribution. Therefore, its application in mechanical reliability research is limited. The so-called lack of "memory" means that a certain product or part is still like a new product after a period of time t0, and does not affect the future working life value, or It is said that after a period of time t0, the life distribution of the product is the same as the life distribution when it was not working. Obviously, this characteristic of the exponential distribution, and the damage process of mechanical parts such as fatigue, wear, corrosion, creep, etc. The actual situation is completely contradictory, which violates the process of product damage accumulation and aging. Therefore, the exponential distribution can not be used as the distribution form of functional parameters of mechanical parts.

Although the exponential distribution can not be used as the distribution rule of mechanical parts' functional parameters, it can be approximated as a high-reliability complex component, machine or system failure distribution model, especially in the whole machine test of components or machines.

The exponential distribution is much slower than the power distribution approaching zero, so there is a very long tail. The exponential distribution is often considered to be a long tail distribution. The degree of penetration of Internet web links is in line with the exponential distribution

The parameter of the exponential distribution is λ, and the expectation of the exponential distribution is 1/λ, and the variance is the square of (1/λ).

C：5

X1：16

X2：23

Click "calculate" to output the result

P (X1 < X < X2)：0

Average: 0.2

Median: 0.1386

Variance: 0.04

Standard deviation: 0.2

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