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EdrawMindProbability Theory and Mathematical Statistics
MindMap Gallery Probability Theory and Mathematical Statistics
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Probability Theory and Mathematical Statistics
A particularly comprehensive mind map that summarizes the basic concepts of probability theory, random variables and their distribution, random vectors, numerical characteristics, mathematical statistics, Point estimate etc.
Edited at 2024-01-13 22:48:46- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- Project Management Process Template
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
Probability Theory and Mathematical Statistics
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- Project Management Process Template
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
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- Outline
Probability Theory and Mathematical Statistics
Basic concepts of probability theory
Four formulas
addition
AUB, AB at least one occurs
Subtraction
division
multiplication
P(AB)=P(A/B)*P(B)
independent
Classical concept
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
Bernoulli profile
Random variables and their distribution
discrete random distribution
tabular method
Be clear and concise in the form of a list
General method
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
Evenly distributed
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 distribution
Find the marginal distribution
Find conditional distribution
Find whether to independently verify whether the union is equal to the product of the edges
continuity
Normative
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.
Conditional Probability
subtopic
Distribution of two-dimensional random vectors
Discrete random variable
continuous random variable
digital features
Expectation and variance
Variance = Expectation of Squares Expectation of Squares
Chebyshev's inequality
discrete covariance
continuity covariance
mathematical statistics
various distributions
central limit theorem
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