Expected Value Practice
Flashcard
•
Mathematics
•
University
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a probability distribution?
Back
A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take. The sum of all probabilities must equal 1.
2.
FLASHCARD QUESTION
Front
What are the conditions for a valid probability distribution?
Back
1. All probabilities p(x) must be between 0 and 1. 2. The sum of all probabilities must equal 1.
3.
FLASHCARD QUESTION
Front
What is a discrete random variable?
Back
A discrete random variable is a variable that can take on a countable number of distinct values.
4.
FLASHCARD QUESTION
Front
What is a continuous random variable?
Back
A continuous random variable is a variable that can take on an infinite number of values within a given range.
5.
FLASHCARD QUESTION
Front
How do you calculate the expected value of a random variable?
Back
The expected value (E) is calculated by summing the products of each possible value and its corresponding probability: E(X) = Σ [x * p(x)].
6.
FLASHCARD QUESTION
Front
What is the expected value of a game where you pay $2 to play, and the outcomes are: lose (red), win $2 (green), win $5 (blue)?
Back
The expected value is -$0.50.
7.
FLASHCARD QUESTION
Front
What does it mean if the expected value is negative?
Back
A negative expected value indicates that, on average, you will lose money if you play the game repeatedly.
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