Fifth chapter stochastic events and their probability _ statistics

1 random events and their probabilities

Trials, Events
Random events (accidental events), inevitable events, impossible events
The properties and algorithms of probability 2 probability

Mutex event: Event A and time B cannot occur concurrently, p (a∪b) =p (a) +p (b) multiplication formula: P (AB) =p (b) p (a| B
When two events are independent, p (AB) =p (B) p (a)
In general, set N events a 1, a 2,..., a n incompatible, P (A i) > (i=1,2,..., N), event B satisfied: B⊂a 1 +a 2 +...+a N, then
P (B) =∑n I=1 p (A i) p (b| A i)
The upper type is called the full probability formula.
The intuitive meaning of a full probability is that an event B occurs for various possible reasons, a I (i=1,2,..., N), and if B is caused by reason a I, the probability of B happening is P (a I B), (i=1,2,..., N). Each A I occurrence can cause B to occur the corresponding probability is P (a I | b), so the probability of the occurrence of B is:
P (B) ==∑n I=1 p (a i B) =∑n I=1 p (a i) p (b| A i)
With the solution of the full probability formula, the Bayesian formula is based on the conditional probability to find the cause of the occurrence of the event, and its formula is described as follows:
Set N Events a 1, a 2,..., a n incompatible, P (A i) > (i=1,2,..., N), event B satisfied: B⊂a 1 +a 2 +...+a N, then
P (A I | B) =p (A i) P (b| A i) ∑n J=1 p (a J) p (b| A j) 3 discrete random variables and their distributions

Expect
Variance: Σ²=d (x) =e[x-e (x)]²=e (x ²)-[e (x)]²
Two distribution: E (x) =NP D (x) =NPQ
Poisson's distribution: The distribution of the number of occurrences of an event within a specified time range or within a specified area or volume.
P (X) =λn e−λn! λ=0,1,2,...
The average number of events within a given time interval, lambda
E (x) =λ,d (x) =λ4 probability distribution of continuous random variable 1 probability density f (x)

2 distribution function

3 Normal Distribution

Definition and characteristics of normal distribution
Standard normal distribution
Normal distribution table
3σ Guidelines
| The probability of x-μ|>3σ is very small, and it can be assumed that the value of x almost certainly falls within the interval (μ-3σ,μ+3σ), which is called the "3σ guideline" in total Quality management.
Normal approximation of two-item distributions