"Using Frequency to Estimate Probability" Probability Preliminary PPT Courseware 2

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"Using Frequency to Estimate Probability" Probability Preliminary PPT Courseware 2

Review the past and learn the new

1. Use frequency to estimate probability

When there are many possible outcomes of the experiment and the likelihood of each outcome occurring is equal, we can derive the probability in the following way. When all possible outcomes of the experiment are not finite, or the likelihood of the various possible outcomes occurring is unequal, We generally have to estimate the probability through statistical frequency.

Under the same conditions, when a large number of repeated experiments are carried out, the probability of a random event occurring can be estimated based on the frequency of a random event gradually stabilizing around a constant P.

For the sake of simplicity, can we directly regard the frequency of citrus damage corresponding to 500 kilograms of citrus in the table as the frequency of citrus damage as the probability of citrus damage?

According to the frequency stability theorem, when the accuracy required is not very high, it may be appropriate to use the frequency in the last row of data in the table to approximately replace the probability.

If you specify two integers, can the computer randomize an integer between those two integers?

You can also use a calculator to generate random integers between two integers you specify (including these two integers). For example, to generate a random integer between 1 and 9, you must first enter the calculator to generate random numbers; then enter the range of random numbers to be generated (1 to 9); press the key repeatedly, and the calculator can Generate the required random numbers.

The random numbers generated by the calculator are a series of numbers obtained using mathematical methods. They have properties similar to random numbers. In fact, dice are the earliest machines that can generate 6 random numbers from 1 to 6.

In the simulation test of estimating probability from frequency, the computer has greater advantages. After generating random numbers, it takes a lot of calculations to obtain the corresponding frequency, but the computer can generate random numbers by itself according to the set program and perform statistics. calculate.

Suppose that during the experiment of using small balls to simulate the problem, 6 black balls are used to replace 3 pairs of black socks, and 2 white balls are used to replace 1 pair of white socks:

(1) Once I found two white balls, but then I forgot to put them back. Will this affect the experimental results?

It has an impact. If you don't put it back, it will not be an experiment of 3 pairs of black socks and 1 pair of white socks, but it will become an experiment of 3 pairs of black socks halfway. The results of the two experiments are different.

(2) If you accidentally get the colors wrong and use 2 black balls and 6 white balls for the experiment, what will be the result?

Class summary

Clarified a relationship------the relationship between frequency and probability

When there are many trials or the sample size is large enough, the frequency of an event will be very close to the corresponding probability. At this time, we can use the frequency of an event to estimate the probability of the event.

Understand a method-------use multiple trial frequencies to estimate probability

Experienced an idea: use samples to estimate the population and use frequencies to estimate probability

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Update Time: 2024-09-04

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