The table of mathematical expectation and variance of commonly used distributions is as follows:

1, 0- 1 distribution: the known random variable x, where P{X= 1}= p, P{X=0}= 1-p, where 0.

2. Binomial distribution: N independent Bernoulli experiments (Bernoulli experiment means that each experiment has two results, and the probability of each result is constant, such as flipping a coin). Where E(X)=np and variance D(X)=np( 1-p).

3. Poisson distribution: its probability function is p {x = k} = λ k/(k! E λ) k = 0, 1, 2...k represents the value of the variable. Where both expectation and variance are λ.

4. Uniform distribution: If the continuous random variable X has probability density, it is said that X obeys uniform distribution on (a, b). Where E(X)=(a+b)/2 and variance d (x) = (b-a) 2/ 12.

5. Normal distribution: If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ2, it is recorded as N(μ, σ2). When μ=0 and σ= 1, the normal distribution is standard normal distribution. Where the expected value is u and the variance is the square of σ.

6. Exponential distribution: If the random variable X obeys the exponential distribution with parameter λ, it is denoted as X~E(λ). The expected value is E(X)= 1/λ, and the variance is D(X)= 1/λ.

The meaning of learning:

1, cognitive self. Knowledge is infinite, so is learning. The more knowledge you learn, the more ignorant you will find yourself. A lot of knowledge is unclear or even unheard of.

2. Improve yourself. In the development of modern society, achievement is not the only way out, but learning is what we want to pursue all our lives.

3. broaden your horizons. Read thousands of books and take Wan Li Road. Learning can add interest to our plain life. Even if you can't take Wan Li Road, you can study thousands of books.

4. satisfy the thirst for knowledge. Everyone has the right to pursue knowledge and the right to choose whether to study. Some people know themselves by learning. Some people improve themselves through learning. Some people broaden their horizons through study.

5. Create more possibilities. The road to learning is difficult, but it is substantial.