📚 Topic Summary
A discrete random variable is a variable whose value can only take on a finite number of values or a countably infinite number of values. These values are often integers, representing counts. When working with discrete random variables, we often look at the probability distribution, which describes the probability associated with each possible value the variable can take. The expected value, variance, and standard deviation are key measures used to summarize the distribution.
For example, consider flipping a coin 3 times. The number of heads you get (0, 1, 2, or 3) is a discrete random variable. Each outcome has a specific probability associated with it, forming the probability distribution.
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Discrete Random Variable |
A. A measure of the spread of a distribution. |
| 2. Probability Distribution |
B. The average value of a random variable, weighted by its probabilities. |
| 3. Expected Value |
C. A variable whose value can only take on a finite or countably infinite number of values. |
| 4. Variance |
D. A function that assigns probabilities to each possible value of a random variable. |
| 5. Standard Deviation |
E. The square root of the variance. |
(Match: 1-C, 2-D, 3-B, 4-A, 5-E)
✍️ Part B: Fill in the Blanks
A __________ random variable can only take on a finite or countably infinite number of values. The __________ __________ describes the probability associated with each possible value of the variable. The __________ __________ is the average value, weighted by probabilities, and the __________ measures the spread of the distribution. We use the __________ __________ to help us interpret the variance.
(Answers: discrete, probability distribution, expected value, variance, standard deviation)
🤔 Part C: Critical Thinking
Give an example of a real-world scenario involving a discrete random variable, and explain how you would calculate its expected value. What does the expected value tell you in this context?