Independent repeated experiment and binomial distribution Is the independent repeated experiment a kind of binomial distribution? If not, what is the difference between them?

Independent repeated experiment and binomial distribution Is the independent repeated experiment a kind of binomial distribution? If not, what is the difference between them?

Independent repeated experiment is to do n times of the same experiment, and each time does not affect each other
Binomial distribution refers to the probability distribution of how many times an event occurs under the premise of independent repeated experiments
They are not the same thing in essence, but they are closely related in theoretical research

The success rate of each experiment was 2 / 3, and the probability of failure in three independent repeated experiments was 1

Consider which failure, so use combination C (3,1)
Then the probability of one failure: C (3,1) * (1-2 / 3) * (2 / 3) ^ 2 = 4 / 9

Expectation in repeated independent experiments
In repeated independent experiments, event a may occur every time
Let X be the number of times until a occurs. Q: e [x | x > 1] = 1 + E [x]

It is established
Intuitively understand this equation, that is to say, after the first experiment did not occur a, it still takes e (x) experiments on average to occur a
That is to say, the result of the first experiment does not affect the later results
It is more convenient to use the following formula (a special case of the full expectation formula) if it is strictly proved:
E(X) = P(X = 1)+P(X > 1)·E(X | X > 1).
The simple proof of the formula is as follows: for k > 1, P (x = k) = P (x = k, x > 1) = P (x = k | x > 1) · P (x > 1)
Therefore, e (x | x > 1) = ∑ {2 ≤ K} K · P (x = k | x > 1) = ∑ {2 ≤ K} K · P (x = k) / P (x > 1)
So p (x > 1) · e (x | x > 1) = ∑ {2 ≤ K} K · P (x = k)
E (x) = ∑ {1 ≤ K} K · P (x = k) = P (x = 1) + ∑ {2 ≤ K} K · P (x = k)
E (x) = P (x = 1) + P (x > 1) · e (x | x > 1)
Note: the above formula does not use the condition of independent repetition
For independent repeated experiments, we know that x obeys the geometric distribution of parameter p (x = 1), e (x) = 1 / P (x = 1)
And P (x > 1) = 1-p (x = 1), e (x | x > 1) = 1 + 1 / P (x = 1) = 1 + e (x)
Of course, it is feasible to calculate e (x | x > 1) directly

Scientific and cultural cultivation is more important than ideological and moral cultivation,
Thank you very much

Moving China 2005 person of the year award winner "Li Chunyan" is the last barefoot doctor in the mountain, carrying a basket to practice medicine in Tianlong. A bamboo building with four windy walls has become the warmest hospital in the world, with a thin shoulder, shouldering the health of ten miles and eight townships
When she decided to work in Guangdong with her husband, when they were about to go out, the villagers arrived just in time. The villagers took out a crumpled one or two yuan and handed it to Li Chunyan: "Doctor Li, you're gone, what can we do?" Li Chunyan didn't leave
The fundamental significance of the cultivation of scientific knowledge and culture lies in the continuous sublimation of one's ideological and moral cultivation, and the use of the scientific and cultural knowledge and mastery for the benefit of society. A person with real knowledge and cultural cultivation should also have lofty ideals and noble ideological and moral values

What does CPK mean?

CPK: abbreviation of complex process capability index, which is used by modern enterprises to express process capability. Process capability is the ratio of the maximum allowable variation range of process performance to the normal deviation of process

What aspects should the author demonstrate the importance of experimental spirit in science

Two
From the two aspects of understanding the connotation of the spirit of learning from things and its important role in science

Can you explain why there is a clock slow effect

As shown in the figure, a train runs to the right at the speed V (V is large enough), and a beam of light on the train starts from a and reflects back to a through B. at this time, imagine that 1. There is an observer on the train, and he must take the train as the reference system; 2. There is another observer, and take the ground as the reference system. At this time, you have to admit that for the time of the whole journey of light, the knot measured by two people

Experimental spirit of the role of scientific development, examples show!

Madame Curie has been engaged in the research of radioactive substances for a long time. In addition to the harsh experimental environment and the lack of strict physical protection, she is often attacked by radioactive elements. As a result, her blood is gradually damaged and she suffers from leukemia. She also suffers from lung disease, eye disease, gallbladder disease, kidney disease, and even mental disorder

What are the sources of clock slow effect and scale contraction effect

I think your question is very much like a philosophical one. I don't think we should discuss relativity as a philosophical one now. Because relativity is not necessarily correct, it is only correct under its several assumptions

Let's take an example. Two famous sayings or proverbs prove the importance of the experimental spirit, that is, the spirit of seeking knowledge from things, in science
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