MindMap Gallery 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 22:48:46This infographic, created using EdrawMax, outlines the pivotal moments in African American history from 1619 to the present. It highlights significant events such as emancipation, key civil rights legislation, and notable achievements that have shaped the social and political landscape. The timeline serves as a visual representation of the struggle for equality and justice, emphasizing the resilience and contributions of African Americans throughout history.
This infographic, designed with EdrawMax, presents a detailed timeline of the evolution of voting rights and citizenship in the U.S. from 1870 to the present. It highlights key legislative milestones, court decisions, and societal changes that have expanded or challenged voting access. The timeline underscores the ongoing struggle for equality and the continuous efforts to secure voting rights for all citizens, reflecting the dynamic nature of democracy in America.
This infographic, created using EdrawMax, highlights the rich cultural heritage and outstanding contributions of African Americans. It covers key areas such as STEM innovations, literature and thought, global influence of music and arts, and historical preservation. The document showcases influential figures and institutions that have played pivotal roles in shaping science, medicine, literature, and public memory, underscoring the integral role of African American contributions to society.
This infographic, created using EdrawMax, outlines the pivotal moments in African American history from 1619 to the present. It highlights significant events such as emancipation, key civil rights legislation, and notable achievements that have shaped the social and political landscape. The timeline serves as a visual representation of the struggle for equality and justice, emphasizing the resilience and contributions of African Americans throughout history.
This infographic, designed with EdrawMax, presents a detailed timeline of the evolution of voting rights and citizenship in the U.S. from 1870 to the present. It highlights key legislative milestones, court decisions, and societal changes that have expanded or challenged voting access. The timeline underscores the ongoing struggle for equality and the continuous efforts to secure voting rights for all citizens, reflecting the dynamic nature of democracy in America.
This infographic, created using EdrawMax, highlights the rich cultural heritage and outstanding contributions of African Americans. It covers key areas such as STEM innovations, literature and thought, global influence of music and arts, and historical preservation. The document showcases influential figures and institutions that have played pivotal roles in shaping science, medicine, literature, and public memory, underscoring the integral role of African American contributions to society.
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