Sophomore at Changchun University of Technology , Probability Theory
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Homework assigned by the teacher = some questions from the textbook + some questions from the teacher
Final exam questions from Homework! After the class, the teacher will send the answer to us. As a senior, I will post it here for your reference. Hit ※ that is the point !
Chapter 1 Basic Concepts of Probability Theory 2, 3, 4
- Probabilistic properties
- Classical Profile
- Conditional Probability
- Total probability and Bayesian formula ※
- independence of events
Chapter 2 Random Variables and Their Distributions 7, 8, 9
1. Definition of discrete random variables, properties, distribution functions, and distribution of functions of random variables
2. Definition of continuous random variables, distribution function and probability density properties, distribution of functions of random variables:
(1) Known probability density f(x) (including undetermined parameter c),
Find: parameter c; find distribution function F(x); find P{a<x<b}; find E(x), D(x) ※
(2) Known distribution function (including undetermined parameter c)
Find: parameter c; find probability density; find P{a<x<b}; find E(x), D(x) ※
(3) Find the distribution of a function of a random variable ※
3. Six common distribution definitions and backgrounds:
0-1 distribution, binomial distribution, Poisson distribution, uniform distribution, exponential distribution, normal distribution
Chapter 3 Distributions of Multidimensional Random Variables 10, 11, 12, 13
- Joint distribution of two-dimensional discrete random variables, marginal distribution law, independence, P{(X,Y)∈G}, distribution of functions of two random variables ※
- Joint distribution of two-dimensional continuous random variables, marginal probability density, independence, P{(X,Y)∈G} ※
Chapter 4 Numerical Characteristics of Random Variables 17
1. Definition and properties of mathematical expectation, variance, covariance, correlation coefficient , moment
2. Numerical characteristics of six common distributions: 0-1 distribution, binomial distribution, Poisson distribution, uniform distribution, exponential distribution, normal distribution
Chapter VI Sample and Sampling Distribution 19, 20
- Common statistics: sample mean, sample variance, sample standard deviation, sample origin moment, sample center distance
- Sampling distribution definition, properties, quantile-
distribution, t-distribution, F-distribution
- Distribution of normal population sample mean
and sample variance
Chapter 7 Parameter Estimation 20, 21, 22, 23, 24
- Point estimation: moment estimation, maximum likelihood estimation *
- Criteria for evaluating estimators: unbiasedness, validity, consistency
- Interval estimation: confidence intervals, one-sided confidence intervals for the mean and variance of a single normal population
Chapter 8 Hypothesis Testing
Hypothesis test for single normal population mean and variance:
Bilateral test, right test, left test ※
