📚 Topic Summary
Independent random variables are variables where the outcome of one doesn't affect the outcome of the other. This means you can calculate probabilities by simply multiplying the individual probabilities together. Understanding this concept is crucial for probability theory and statistics. Let's practice!
🧠 Part A: Vocabulary
Match each term with its definition:
- Random Variable
- Independence
- Probability Distribution
- Expected Value
- Variance
Definitions:
- A function that assigns probabilities to different outcomes.
- The average value of a random variable over many trials.
- The extent to which the occurrence of one event affects the probability of another event. (Absence of influence)
- A variable whose value is a numerical outcome of a random phenomenon.
- A measure of the spread or dispersion of a set of data points around their mean value.
📝 Part B: Fill in the Blanks
When two random variables, X and Y, are __________, the probability of both X and Y occurring is the __________ of their individual probabilities. This means that $P(X=x, Y=y) = P(X=x) * P(Y=y)$. In this case, knowing the value of X provides _____ additional information about the value of Y.
🤔 Part C: Critical Thinking
Give a real-world example of two independent random variables, and explain why they are independent.