4. There are some balls with the same size in the bag, among which 1 ball number is 1, 2 balls number is 2, 3 balls number is 3, and n balls number is n. Choose one ball from the bag and take its number as a random variable to find the probability distribution and expectation.

1 1, a batch of diameter normal distribution N(0.8, 0.02? ) (unit: cm). So how many parts are less than 0.79cm in diameter?

(Note: Questions 5 and 10 have graphs, so they are not answered. )

B 1。 Take any two of n numbers 1, 2 and 3, ..., n, and find the mathematical expectation of the product of these two numbers.

2. A unit, 1000 people go for blood tests, and these people's blood tests can be conducted in two ways:

(1) Everyone's blood is tested separately, so it needs to be tested 1000 times.

(2) Divide each person's blood sample into two parts, take one blood sample of K people, and mix them together for testing. If the result is negative, it is enough to test K people only once; If the result is positive, another blood sample of person K will be tested one by one. At this point, k people need to be tested k+ 1 time.

Assuming that the probability of all people's positive test results is 0. 1, and their reactions are independent, try to compare the number of tests required by the two methods. Make a general discussion on this problem.