Probability theory and distribution function of mathematical statistics random variable First of all, the definition is as follows: FX (x) = P ({w belongs to R: X (W))

It is expressed as A-0 because F may be discontinuous, for example, discrete data. That is to say, if there are only half of 0 and half of 1, then f (x) is 0 in X from negative infinity - 0 - and 1 / 2 in 0 +

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1. Probability theory and distribution function of random variables in mathematical statistics Let the distribution law of random variable X be X -1 2 3 p 0.25 0.5 0.25 Finding P {2 ≤ x ≤ 3} through the distribution function of X The solution is p {2 ≤ x ≤ 3} = f (3) - f (2) + P {x = 2} I want to ask why we add "P {x = 2}" and what is the relationship between the equal sign of 2 ≤ x ≤ 3
2. Probability theory and distribution function of mathematical statistics The absolute value of random variable x is not greater than 1, P {x = - 1} = 1 / 8, P {x = 1} = 1 / 4; in the event {- 1} In order to attract the audience, specially register a new number to send points~
3. Probability density function and distribution function of random variables Let the probability density function of two-dimensional random variables (x, y) be xe^(-y),0
4. Let the random variable x ~ U (0,1), try to find: (1) the distribution function and density function of y = e ^ X; (2) the distribution function and density function of Z = - 2x
5. Let x ~ U (0,1) be a random variable and find the density function of y = - INX RT
6. Let x ~ U (- 1,1) be the random variable, and find the density function of y = e ^ X
7. Let the distribution function of continuous random variable X be f (x), and the density function be f (x), then why is p (x = x) = 0?
8. Let the distribution function of random variable X be f (x) = a + the distribution function of known random variable X be f (x) = a + B arctanx, find the values of a and B, and find P (- 1) （1）∵F(-∞)=0，F(+∞)=1 im(x→-∞)F(x)=A-Bπ/2=0; LIM (x → + ∞) f (x) = a + B π / 2 = 1; why use a minus sign and a plus sign here? How does π / 2 come from How can A-B π / 2 = 0 be solved? Bπ/2=1/2？ Why?
9. Let the probability density of random variable X be f (x) = {x, 0 ≤ x ＜ 1; 2-x, 1 ≤ x ＜ 2; 0, others} to find the distribution function f (x) of X,
10. The density function of random variable x is f (x) = 1 / 2E ^ - | x |, X belongs to R, find the distribution function of X
11. In probability theory, if the probability density f (x) of continuous random variable changes the value of finite points of F (x), f (x) is still the probability density. Why?
12. Probability theory: let the probability density of random variable X be f (x) = {A / X & # 178;, x > 10; 0, X
13. If the random variables X and y are independent of each other and obey the uniform distribution on the interval (0,1), then the following random variables obey the uniform distribution A.x & # 178; b.x + y, C. (x, y) d.x-y, please give me a process,
14. Let the random variables X and y be independent and obey the uniform distribution on the interval [0, a], and then calculate the probability density of the random variable z = x / y
15. Suppose that the random variable x obeys the uniform distribution on the interval [- 1,1], then the probability density of y = 2-x is obtained
16. Let X and y be independent random variables, and obey the uniform distribution on the interval (0,2), then the probability density of Z = x / y is obtained
17. 1. Let the random variable x obey the uniform distribution on the interval (0,2), and try to find the probability density of the random variable y = x2. (X2 is the square of X, and the small 2 above cannot be found on Baidu.) 2、
18. Suppose that the random variables X and y are independent of each other and obey the uniform distribution on [0,1], the probability density of X + y is obtained
19. Suppose that the random variables X and y are independent of each other and obey the uniform distribution on [- 1,1], the probability density of X and Y is obtained The random variables X and y are independent of each other and obey uniform distribution on [- 1,1]. The probability density of X and Y is calculated
20. In the interval [- 1 / 2,1 / 2], take a number x randomly, so that the probability of cos π X between 1 / 2 and √ 2 / 2 is 0 A 1/6 B 1/5 C 1/4 D 1/3