Basic concepts of probability theory
Four formulas
addition
AUB, AB at least one occurs
Total probability, Bayesian formula
Pairwise mutually exclusive: two sets have no intersection
total probability formula
Bayes' formula: the probability of the first small event occurring when a complex event occurs
Random variables and their distribution
discrete random distribution
tabular method
Be clear and concise in the form of a list
binomial distribution
Maximum number of successes
Distribution of continuous random variables
X~U(a,b) is uniformly distributed
X~E(m) is an exponential distribution
X~N(u,6) is a normal distribution
X~b(1,p) is a two-point distribution
X~b(n,p) is a binomial distribution
normal distribution
Chart method
Exploiting the symmetry of normal distribution images
Standardization method
Convert normal distribution into standard normal distribution
Distribution of discrete random variable X
Distribution of continuous random variable X
random vector
two-dimensional random variable
Discrete
Find the marginal distribution
Find conditional distribution
Find whether to independently verify whether the union is equal to the product of the edges
continuity
The probability that the joint distribution is on a certain interval
edge density function
The marginal density function of y can be roughly regarded as the integral of x when y is fixed.
Distribution of two-dimensional random vectors
continuous random variable
digital features
Variance = Expectation of Squares Expectation of Squares
point estimate
distance estimation method
maximum likelihood estimation
The samples are independent and identically distributed
Both the normal distribution and the chi-square distribution are additive
Irrelevance cannot lead to independence. Independence must not be relevant.
The words "at least" and "at most" appear to take advantage of opposing events.
Included here are geometric sketches
1. Analyze the number of variables it includes
2. List and solve geometric relationships
1. Divide the problem into two stages. For example: stage one is picking people, stage two is the probability of color blindness.
2. Let the events be A, B, C, etc.
3. Use total probability or Bayesian formula to solve
Whatever you ask for, get it