📚 Topic Summary
A Probability Mass Function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value. In simpler terms, for a discrete random variable, the PMF tells you how likely each possible outcome is. It's essential to remember that the sum of the probabilities for all possible values must equal 1.
For example, if you flip a fair coin, the PMF would tell you the probability of getting heads (0.5) and the probability of getting tails (0.5). Let's practice calculating these probabilities with a short quiz!
🔤 Part A: Vocabulary
Match the following terms with their correct definitions:
| Term |
Definition |
| 1. Discrete Random Variable |
a. A function that gives the probability that a discrete random variable is exactly equal to some value. |
| 2. Probability Mass Function (PMF) |
b. A variable whose value is a numerical outcome of a random phenomenon that can only take a finite number of values or a countably infinite number of values. |
| 3. Outcome |
c. The set of all possible results of a random experiment. |
| 4. Sample Space |
d. The result of a single trial of an experiment. |
| 5. Event |
e. A set of outcomes to which a probability is assigned. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: discrete, 1, probability, PMF, and random variable.
A __________ is a function that assigns a __________ to each possible value of a __________ . The sum of all probabilities in a __________ must equal __________. This applies specifically to variables that are __________.
🤔 Part C: Critical Thinking
Describe a real-world scenario where using a Probability Mass Function (PMF) would be helpful. Explain what the discrete random variable would be in that scenario and what kind of insights the PMF could provide.