Solving Graduate School Mathematics Probability Problems? Postgraduate Probability Theory Questions

I don't know what your problem is, how to solve it?

Nine mindsets for probabilistic problem solving.

The first sentence: if the requirement is the probability of "at least" one of several events occurring, the probability addition formula immediately comes to mind; When groups of events are independent of each other, the probability formula for opposing events is used.

Sentence 2: If the given test can be broken down into (0-1) n-fold independent repeat tests, then the Bernoulli test and its probability calculation formula are immediately reminiscent.

Sentence 3: If an event occurs with the occurrence of a complete set of events, then the probability of occurrence of the event is immediately associated with the calculation of the full probability formula. The key: Look for a complete set of events.

Sentence 4: If the random variable x n is given in the problem, then the normalization n(0,1) is immediately associated with the problem.

Sentence 5: The problem of finding the density of the edge distribution of the two-dimensional random variable (x,y) should immediately be associated with first drawing the region where the density of the joint distribution is made, then determining the variation interval of x, and then drawing a straight line on the y-axis in this interval, first intersecting the boundary of the region is the lower bound of y, and the latter is the upper limit, and the method is similar.

Sentence 6: To find the probability that the two-dimensional random variable (x,y) satisfies the condition y g(x) or (y g(x)) should immediately be associated with the calculation of the double integral, where the integration domain d is the common part of the plane region of the joint density and the region satisfying y g(x) or (y g(x)).

Sentence 7: The problem involving the numerical characteristics of the number of times an event occurs n times is immediately associated with (0-1) decomposition of x.

Sentence 8: If it is a simple random sample of the population x, then the distribution of statistics is generally associated with the definition of chi-square distribution, t-distribution and f-distribution. For more skills, you can also pay attention to Beijing New Oriental's postgraduate mathematics course.

The number of people obeys the Poisson distribution, which means that the probability of the number of people = xx obeys the Poisson distribution when the number of people is unknown. And the mention has clearly told you that there are n people in total. Therefore, the condition that 'the number of people obeys the Poisson distribution' is redundant and has no value.

p refers to the probability that y=m occurs under the premise of x = n.

p refers to the probability that y=m and x=n occur at the same time.

p represents the probability that the number of passengers at the starting point is n, and the number of people getting off the bus is m, and p=, which is also based on this to ask the second question.

It's another way of writing permutations and combinations.

Two-dimensional normal distribution.

Knowledge requirements. 1.A sufficient and necessary condition for the independence of the two-dimensional normal distribution.

2.Integral. 3.Normal distribution standard morphology.

4.Finding the expected variance of a random variable.

5.Generalized random variables.

Multiply the two functions and you'll see it clearly.

Take the interval problem, -2 x 2, x x - and -2 take the small interval. The result is [-2,-.

x obeys the normal distribution, the mean is 6, the variance is 4, the standard deviation is 2p(4<=x<=8) = p(6-2<=x<6+2)=