Glossary
Continuous Random Variable
A random variable that can take any value within a given range or interval.
Example:
The exact time it takes a student to complete a quiz is a continuous random variable, as it could be 15.34 minutes, 15.345 minutes, etc.
Discrete Random Variable
A random variable that can take on a countable number of distinct values, often integers.
Example:
The number of red cars passing a specific intersection in an hour is a discrete random variable because you can count them (0, 1, 2, ...).
Mean or Expected Value (E(X))
The long-run average outcome of a random variable over many trials, calculated by summing each outcome multiplied by its probability.
Example:
If a game has an expected value of 1.50 per game if you played it many, many times.
Parameter
A numerical characteristic that describes an entire population.
Example:
The true average height of all high school seniors in the U.S. is a parameter.
Random Variable
A numerical outcome from a random event or phenomenon.
Example:
The number of times a student checks their phone during a 30-minute study session is a random variable.
Standard Deviation (SD(X))
The square root of the variance, representing the typical distance of values from the mean in the original units of the random variable.
Example:
If the standard deviation of test scores is 5 points, it means that typical scores are about 5 points away from the average score.
Variance (Var(X))
A measure of how spread out the values of a random variable are around its mean, calculated as the average of the squared differences from the mean.
Example:
A high variance in daily stock price changes indicates that the stock's price fluctuates widely from its average change.