> For the complete documentation index, see [llms.txt](https://kmis.gitbook.io/statistics/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://kmis.gitbook.io/statistics/chapter-4.-discrete-random-variables/4-1.-random-variables.md).

# 4-1. Random Variables

随机变量

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Chapter 4-1 (Korean)
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Chapter 4-2 (Korean)
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Chapter 4-3 (Korean)
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Chapter 4-1 (Chinese)
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Chapter 4-2 (Chinese)
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Chapter 4-3 (Chinese)
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Examples of Chapter 4-1
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Examples of Chapter 4-2
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Examples of Chapter 4-3
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Examples of Discrete Distribution Functions of Rstat
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> *A* **random variable** *is a numerical quantity that is generated by a random experiment.*

We will denote random variables by capital letters, such as $$X$$ or $$Z$$ , and the actual values that they can take by lowercase letters, such as $$x$$ and $$z$$ .

| Experiment                                  | Number $$X$$                                | Possible Values of $$X$$           |
| ------------------------------------------- | ------------------------------------------- | ---------------------------------- |
| Roll two fair dice                          | Sum of the number of dots on the top faces  | 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 |
| Flip a fair coin repeatedly                 | Number of tosses until the coin lands heads | 1, 2, 3,4, …                       |
| Measure the voltage at an electrical outlet | Voltage measured                            | $$118 ≤ x ≤ 122$$                  |
| Operate a light bulb until it burns out     | Time until the bulb burns out               | $$0 ≤ x < ∞$$                      |

> *A random variable is called* **discrete** *if it has either a finite or a countable number of possible values.*&#x20;
>
> *A random variable is called* **continuous** *if its possible values contain a whole interval of numbers.*

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Discrete Random Variables
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