1, exchange law, association law, distribution rate, Morgan's law; (the basis of solving problems)
2. Classical probability-finite equal possibility, geometric model-infinite equal possibility;
3, the principle of drawing lots-has nothing to do with the order;
4, the principle of small probability-small probability events can't happen in a test, once it happens, it will doubt the correctness of the realization law;
5. Conditional probability: Note that the probability of a condition must be greater than 0;
6. Overview: Cause > Result Bayesian: Result >; Reason;
7. Compatibility is defined by events and independence by probability.
chapter two
The values of 1, 0- 1 distribution, binomial distribution and Poisson distribution all start from 0;
2. The distribution function is right continuous, and the distribution function should be written as right continuous as far as possible;
3. Properties of distribution function and probability density;
4. The probability of any specified value of continuous random variable is 0;
5. A probability of 0 is not necessarily an impossible event, and a probability of 1 is not necessarily an inevitable event;
6. The graphic characteristics of normal distribution;
7. Try to find the distribution of the function according to the definition method, and write the basic formula according to the definition;
8. When the segmentation is monotonous, the formula should be used in segments and then added.
Chapter III (This chapter is prone to mistakes)
1, the properties of two-dimensional distribution function; (Not a subtraction function instead of a single increasing function; Right continuous)
2, the distribution function must be defined, pay attention to drawing the right picture;
3. When calculating the edge distribution, pay attention to where the intervals of different variables are used; To find the edge distribution of X, divide the interval of X first, and then integrate all intervals of Y in different intervals (Y may have different function expressions in different intervals).
4. The integral of negative semi-t square of e from negative infinity to positive infinity; (Zhesan P83)
5. The conditional probability is the same, so pay attention to the corresponding interval; I'm sorry to lose points on the details of this problem.
6. What is the situation that Max (x, y) and min(x, y) are independent of each other? What is independent and identically distributed? (see 08 multiple choice questions)
7. Generally, the edge distribution can only be determined when the variables are independent of each other.
chapter four
1, the series is absolutely convergent and expected to exist;
2. Expected sum equals expected sum, and there is no need for relationship between xy; Expected product equals expected product, and xy should be independent of each other;
3. Zhejiang III P 120: the idea of decomposition, and P126;
4. Variance sum is different between independent and dependent time;
5. Independent launch is irrelevant; Independence cannot be inferred from irrelevance; Uncorrelated is only linearly uncorrelated; If the relationship between xy in the topic can be expressed (generally), it is not independent;
6. Two-dimensional normal distribution and independent uncorrelated equivalence;
7. Tip: Symmetry can sometimes be used when solving some integrals;
8. Count one, 400 questions. In that comment, P 140, T(4)=3! (If you can use it, it will be very convenient to do the problem.)
chapter five
1, Chebyshev's law of large numbers conditions: independent of each other, consistent with the existence of variance and upper bound;
2. The conditions of Qin Xin's law of large numbers: independence, identical distribution and expected existence;
3. Let's look at binomial distribution, Poisson theorem and Laplace theorem of large numbers.
Chapter vi
1, the variables of the sample are independent and identically distributed;
2. Statistical data does not contain unknown parameters;
3. See the last line of last year's real question for the expectation and variance of X2 distribution;
4. look at the symmetry formula of symmetry a of t distribution diagram;
5. We must master three forms of distribution;
6.P 168 is very helpful for later investigation and prediction.
Chapter VII
1, the moment estimation is the expectation of x to the power of 1, 2;
2. Maximum likelihood estimation! The two methods of maximum likelihood estimation can be combined; (Open your mind)
3. Interval estimation; If you can read a good book, it is not difficult to understand, otherwise there is nothing to read by copying P205. )
Chapter VIII
1. The sign of the rejected domain is the same as that of the alternative hypothesis P229.
2.P436 expectation and variance;