📚 Topic Summary
Discrete probability distributions describe the probability of each outcome in a discrete random variable. A discrete random variable is one where the value can only take on a finite number of values or a countably infinite number of values. Common examples include the number of heads in a series of coin flips (Binomial), the number of trials needed for the first success (Geometric), and the number of events occurring in a fixed interval (Poisson). Understanding these distributions allows us to make predictions and analyze data in various real-world scenarios.
A probability mass function (PMF) is often used to represent a discrete probability distribution. The PMF gives the probability that a discrete random variable is exactly equal to some value.
🧮 Part A: Vocabulary
Match the term to its definition:
- Term: Random Variable
- Term: Probability Mass Function (PMF)
- Term: Discrete Distribution
- Term: Expected Value
- Term: Variance
- Definition: A function that gives the probability that a discrete random variable is exactly equal to some value.
- Definition: A variable whose value is a numerical outcome of a random phenomenon.
- Definition: A probability distribution where the variable can only take on a finite or countably infinite number of values.
- Definition: A measure of the spread or dispersion of a random variable's possible values around its mean.
- Definition: The weighted average of the possible values of a random variable, where the weights are the probabilities of the values.
(Match the terms to the definitions. The answers are scrambled for a challenge!)
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: discrete, probability, random, outcomes, variable.
A __________ distribution describes the __________ of different __________ for a __________ __________ . Each outcome has a specific __________ associated with it.
🤔 Part C: Critical Thinking
Give a real-world example where understanding discrete probability distributions can be valuable. Explain why.
