For example, you have some spare money and two investment schemes.
First, the income is very stable, with a 100% net profit of 50,000.
Second, instability, 50% chance to earn 200,000, and 50% chance to lose 654.38+ 10,000.
If calculated from the mathematical expectation formula, both of them make a profit of 50 thousand. But these two schemes are different, and there are great differences. Where are the details?
First, the income stability of the two schemes is different, the first one is very stable, and the second one fluctuates greatly.
Therefore, different mathematical expectations do not mean that two things are of the same value. The fluctuation degree of random results also has a great influence on the value of a thing and our decision.
When describing and thinking about a * * * random event, we have to consider this volatility, which involves a professional concept called variance.
Variance describes the fluctuation range of random results around mathematical expectations.
The greater the variance, the greater the volatility of things. Risk, in essence, refers to volatility. Therefore, the essence of variance is a measure of risk. The greater the variance of a random event, the farther the possible result is from the expected value, and the greater his risk.
When Ren was young, he had a family leave once a year. He couldn't see his children for 330 days a year, and he looked at them every day for the remaining 30 days. If he goes home once every 1 1 day, the variance will be much smaller.
Variance itself is neutral, it doesn't matter whether it is good or bad, but in our own life, we can really fight against variance through different strategies.
First of all, we can fight against variance by increasing costs.
The more capital, the stronger the ability to take risks. With enough capital, it is possible to continue the game and strive for mathematical expectations.
For other problems in life, similar to increasing costs, as long as data selection is increased, variance and fluctuation can be countered.
For example, it is too risky to predict the enrollment rate of a school's college entrance examination only by looking at the achievements of a certain student or a certain class. In case we happen to meet a class that is a master learner, we can make a more accurate prediction by increasing the amount of data and collecting the comparative data of the whole school or the whole province and the whole country 10 classes.
On the contrary, we can also use variance to achieve our goal by thinking that design actively expands volatility.
Distance, why do you know that lottery is a loss-making business and lottery tickets can still be sold all over the world?
Because of the huge variance of lottery tickets, most people didn't win the prize, but the winners got extremely high bonuses. The variance is set to 0, the bonus is a few cents, and no one buys it. ?
Today, I learned variance thoroughly, and I wrote a whole reading note. I still don't know what special variance is, what's the use of variance, and how to calculate this damn variance. . . . . Looking through the catalogue of probability, there are normal distribution, power law distribution, Poisson distribution, hypothesis testing, Bayesian reasoning and so on. Who knows where the tears of joy I saw in probability class came from?