Random variable

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/random-variable

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the foundational work?Measure-theoretic probability by Andrey Kolmogorov in the 1930s
2. What is the key mathematical properties?Characterized by their probability distribution (PMF for discrete, PDF for continuous)
3. Why do we use random variables in science and money?They help us measure uncertainty, so scientists and bankers can predict things like how many cars will pass or how much a stock might be worth.
4. How did people first think about random variables?In the 1600s, mathematicians like Pascal and Fermat studied games of chance, and later, Kolmogorov in the 1900s made the idea precise with math.

Sample Space: The set of all possible outcomes of a random experiment.
Probability Mass Function (PMF): Assigns probabilities to each possible value of a discrete random variable.
Probability Density Function (PDF): Describes the relative likelihood for a continuous random variable to take on a given value.
Expected Value: The weighted average of all possible values of a random variable, representing its long-run average.