As expected, there is no difference between the two schemes, both of which are 500 thousand. However, mathematical expectation is a quantitative measure of the long-term value of random events. In terms of volatility, the second scheme is too volatile and easy to lose money.
Therefore, the scheme 1 is a more suitable choice.
But on the other hand, you also understand the diversification of the portfolio. It is often said that eggs are not put in one basket, which reduces risks and fluctuations. Those who truly grasp wealth and invest successfully may need to fluctuate and put their eggs in one basket, so as to obtain excess returns. Because generally speaking, the fluctuation is reduced, and the possibility of maximum income is also reduced. The risk is not terrible, the key is whether the risk is worthy of the income.
In addition, in daily life, do you want to know whether it will rain tomorrow and whether you should take an umbrella when you go out? Or judge the future ups and downs of the stock market, whether to add positions or sell them; Whether you want to know when the COVID-19 epidemic will pass, or you want to choose the most effective scheme to implement it ... All these, as long as they involve decision-making, actually need to judge the probability. If you master probabilistic thinking, you can make correct decisions and seize opportunities now and in the future.
The second question I am asked the most is, is probability theory particularly difficult? Is the calculation complicated? But this is actually, this is our misunderstanding.
Because, first of all, learning probability theory does not require a high level of mathematics.
Simple probability calculation is actually very simple. Why do you say that? Give a simple example and you will understand.
The Lao Wang family has two children. It is understood that the boss is a girl. What is the probability that the other person is a boy? It's simple. The gender of the boss has been determined. The second child is either a boy or a girl, so the probability that the other child is a boy is 1/2. However, as long as you change a word in the condition and change "the boss is a girl" to "one of them is a girl", you change a word, and then the probability changes. One of them is a girl, two children have three situations of "girl boy, boy girl, girl girl", and two children are boys, so the probability of the other boy increases immediately, from 1/2 to 2/3. Isn't it amazing?
In fact, when solving many probability problems, it is more about testing your Chinese ability to see if you can correctly understand the meaning of the questions and find the conditions. Many people can't solve probability problems, not because they can't calculate, but because they don't carefully examine the problems and don't understand the meaning of the problems. What really defeated them was not the lack of mathematics, but the lack of Chinese ability.
In reality, the first step in making decisions with probabilistic thinking is to turn a realistic problem into a correct probabilistic problem, which also tests the ability to understand the problem and grasp key information, so it is very important to have a certain knowledge of Chinese.
As long as you have a certain language ability, learning probability theory will be very advantageous. Believe me, as long as you pass the Chinese exam, you will know the basic operations of addition, subtraction, multiplication and division, and you will understand my lecture hall on probability theory.
Second, each of us has a sense of probability, but we have not formed a systematic thinking.
When friends have bad luck one after another, we will comfort them by saying, "Don't come too late, the bad luck will always pass"; Investing in financial management, seeing that everyone began to flock to buy stocks and invest in funds, they knew that "the risk is getting bigger and bigger and they must quit." You see, everyone has this superficial sense of probability.
There is a very interesting joke on the Internet:
The scum with the lowest score in the class found the scum with the second lowest score and said, let me copy the answers to the exam later! The penultimate slag is very happy, thinking that I am not the worst, not as good as learning to bully, but better than the last one. As a result, the exam results came out. The second-to-last scum got the last place, and the second-to-last scum got the middle score. Why? The penultimate slag said that after we ruled out our own answer, the possibility of choosing the right answer really improved.
Even scum have fragmented probabilistic thinking, and of course we have more. It's just that they are scattered in our minds and lack systematic arrangement.
And this book is to help you finish the sorting work and help you piece these pieces together into a set of systematic thinking.
Third, this "Liu Jia Lecture Notes on Probability Theory" is about general knowledge, not formulas.
In this book, I won't explain complicated formulas to you too much, but show you the whole picture of probability theory from a general angle. Let you quickly understand the young, basic and very important branch of mathematics in the shortest time.
As a teacher of Nanjing University, probability theory is my old job. I am the winner of the first National Award Scheme for Excellent Computer Teachers in Colleges and Universities. At the same time, I am also a special teacher of MBA and EDP (senior manager development course) in Nanjing University Business School. I am good at making abstract mathematics lively and interesting, so that you can understand it and get some inspiration. I am your bridge to probability theory, and cultivate probabilistic thinking.
This lecture on probability theory comes from the course I got in the station, but in the process of publishing the book, we made many supplements and adjustments. Basically, more cases are added to each part, as well as the topic of specific application probability, and even the structure and narrative context of the whole content have been adjusted. So the book you see is an iterative book with richer content and more complete system.
There are also many books on probability theory on the market, and I have read different books when I was teaching. However, we have never found a book on probability theory that is particularly easy to read and suitable for the general public to understand.
So, I was very happy when this book was published. It can fill this gap to some extent. On the one hand, it covers almost all the basic knowledge points of probability theory, including concept, calculation and application. It is a real lecture on probability theory. On the other hand, through simple language and vivid and interesting cases, you can understand the ideas behind probability theory and form a probabilistic way of thinking.