今天是:2024年12月4日 星期三
中文版 >
1.1.03 Sample space
正文

  Although the outcome of a randomized trial is uncertain, all possible outcomes are clear.

  We call each possible outcome of a random experiment a sample point , and all of them are called the sample space , denoted as ( or ) .
   For example: (1) In the experiment of tossing a coin and observing whether it appears heads or tails, there are two sample points: heads and tails, and the sample space is

head side, tail side .

If you remember

( front ) , ( tail ) ,

then the sample space can be recorded as

[ Coin tossing test ]

  (2) Observe the number of calls received by a telephone exchange in a day. Its sample points have an infinite number of ( ) times, so the sample space can be abbreviated as

.

  (3) Randomly select one light bulb from a batch and test its life. There are infinite ( and uncountable ) sample points : hour, then the sample space can be abbreviated as

.

  (4) Suppose the random experiment is to randomly pick two balls from a bag containing three white balls ( marked as ) and two black balls ( marked as ) .
  ① If you observe the colors of the two balls taken out, the sample point is

( two white balls ) , ( two black balls ) , 

( one white and one black ) ,

therefore, the sample space is

.

  ② If we observe the numbers of the two balls taken out, the sample point is

( take out the and balls ) ,

since the balls have different numbers, we can assume

, .

Therefore, the sample space has a total of sample points , and the sample space is

.

  Note: This example illustrates that for the same random experiment, the sample points and sample space of the experiment are determined based on the content to be observed.

点评:0