4-1. Random Variables

随机变量

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.
A random variable is called continuous if its possible values contain a whole interval of numbers.

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