🎲 Session 2.9 - Random Variables

What Is a Random Variable?

A random variable is a function that assigns a number to each outcome of a random experiment.

Notation: We usually use uppercase letters like X for a random variable and lowercase letters like x for its value.

🔢 Two Types of Random Variables

Discrete: Countable outcomes (e.g., number of scratches, error bits)
Continuous: Measurable outcomes with decimals (e.g., temperature, voltage)

Sometimes we treat large-range discrete variables like continuous ones for convenience.

📏 Example 1 – Continuous Variable

Experiment: Measure the current in a wire.
Variable: X = current in milliamperes

It could be 2.14, 2.15, 2.16... all values in an interval → continuous

💻 Example 2 – Discrete Variable

Experiment: Count error bits in data transmission.
Variable: X = number of errors
Possible values: 0, 1, 2, 3... → discrete

🛠️ Example 3 – Mixed Precision

Experiment: Voltage measured to nearest 0.01 volt
Values are: 4.10, 4.11, 4.12...
Technically discrete, but we can treat it as continuous in many cases.

🧪 Practice Problem

Which of the following are discrete or continuous?

Time it takes for a machine to finish a job
Number of calls received by a call center in one hour
Proportion of defective bolts in a batch of 500
Voltage measured across a resistor

1. Continuous
2. Discrete
3. Discrete
4. Continuous