📚 Topic Summary
Expected Value (EV) is a fundamental concept in probability and statistics. It represents the average outcome you'd expect if an event were to be repeated many times. For a discrete random variable, EV is calculated by multiplying each possible outcome by its probability and then summing these products. Understanding EV is crucial for decision-making in various fields, including finance, gambling, and insurance.
An Expected Value Worksheet for University Statistics Practice Problems provides structured exercises to reinforce this concept. These worksheets typically include vocabulary matching, fill-in-the-blank questions, and critical thinking problems to ensure a comprehensive understanding of expected value and its applications.
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Random Variable |
A. The sum of all possible values, each multiplied by its probability. |
| 2. Probability |
B. A variable whose value is a numerical outcome of a random phenomenon. |
| 3. Expected Value |
C. A measure of the likelihood that an event will occur. |
| 4. Outcome |
D. The result of a single trial of a random experiment. |
| 5. Discrete Variable |
E. A variable whose value can only take on a finite number of values or a countably infinite number of values. |
(Answers: 1-B, 2-C, 3-A, 4-D, 5-E)
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
The __________ of a random variable is a weighted average of its possible values. Each value is weighted by its __________. For a discrete random variable, the expected value is calculated by summing the product of each __________ and its corresponding __________. The expected value helps in making informed __________ in situations involving uncertainty.
(Answers: Expected Value, Probability, Outcome, Probability, Decisions)
🤔 Part C: Critical Thinking
Consider a game where you flip a coin. If it lands heads, you win $5. If it lands tails, you lose $3. What is the expected value of playing this game? Would you play this game repeatedly? Explain your reasoning.
(Answer: EV = (0.5 * $5) + (0.5 * -$3) = $2.5 - $1.5 = $1. Yes, playing the game repeatedly would likely result in a net gain over time, as the expected value is positive.)