The normal distribution with expectation and variance is recorded. Normal distribution is widely used. Normal distribution can also be used as an approximation of binomial distribution under certain conditions.
The exponential distribution is an asymmetric distribution with one parameter, and the probability density function is:
The mathematical expectation is that the variance is 0. Exponential distribution is the only memoryless continuous random variable, which is widely used in queuing theory and reliability analysis.
Gamma distribution is an asymmetric distribution with two parameters, which is recorded as expected. Time degenerates into exponential distribution. The sum of two independent exponential distributions with the same distribution (parameters) is a gamma distribution. Gamma distribution can be used for service time, part life, etc.
Gamma distribution is also called Erlang distribution.
Weibull distribution is an asymmetric distribution with two parameters, which is recorded as. Time degenerates into exponential distribution. As equipment, the life distribution of parts is widely used in reliability analysis.
Beta distribution is a two-parameter, non-uniform distribution in the interval, which is recorded as.
Bernoulli distribution is a two-point distribution with a value probability of sum, which is recorded as. Used for basic discrete models.
Poisson distribution is closely related to exponential distribution. When the average arrival rate of customers is constant and the arrival interval obeys exponential distribution, the number of customers arriving per unit time obeys Poisson distribution, that is, the probability of arriving at customers per unit time is:
Remember that Poisson distribution is widely used in queuing service, product inspection, biological and medical statistics, astronomy, physics and other fields.
In each independent experiment, if the probability of an event is 0, then the number of occurrences of the event in the next experiment obeys binomial distribution, that is, the probability of occurrence is:
Remember that binomial distribution is the sum of an independent Bernoulli distribution. It is widely used in product inspection, insurance, biological and medical statistics.
When it is large, it is similar to normal distribution; When large, small and approximate are constant, approximate