Ex and dx of exponential distribution;

When x and y are irrelevant, E(XY)=E(X)E(Y) and d (x) = e (x 2)-(e (x)) 2. At this time, e (x (x+y-2)) = e (x 2+xy-2x.

D(x) refers to variance, and E(x) refers to expectation. Variance is a measure of dispersion when probability theory and statistical variance measure random variables or a set of data. Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value).

In probability theory and statistics:

Exponential distribution (also called negative exponential distribution) is a probability distribution that describes the time interval between events in Poisson process, that is, the process in which events occur continuously and independently at a constant average rate. This is a special case of gamma distribution. It is a continuous simulation of geometric distribution and has the key characteristic of memoryless. Besides analyzing Poisson process, it can also be found in various other environments.

The addition formula of exponential distribution: f (x) = λ e (-λ x).

Normal distribution is the distribution of all large samples whose distribution tends to the limit, which belongs to continuous distribution. Both binomial distribution and Poisson distribution are discrete, the limit distribution of binomial distribution is Poisson distribution, and the limit distribution of Poisson distribution is normal distribution. That is, np=λ, which can be approximately equal when n is large.

An important feature of exponential function;

It is memoryless (also called memory loss). This means that if a random variable is exponentially distributed, when s, t >; 0 has p (t > T+s | T & gt； T)= P(T & gt； S). That is, if t is the life of a component, it is known that the component has been used for t hours, then the conditional probability that it will always be used for at least s+t hours is equal to the probability that it will be used for at least s hours from the beginning of use.