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Probability

Expected Value

Concept Quizzes

Expected Value - Definition
Expected Value - Properties
Linearity of Expectation
Expected Value - Independent Variables
Expected Value - Problem Solving

Challenge Quizzes

Expected Value: Level 2 Challenges
Expected Value: Level 3 Challenges
Expected Value: Level 4 Challenges
Expected Value: Level 5 Challenges

Expected Value - Problem Solving

What is the expected number of coin flips we must make, before we see a Head followed immediately by a Tail?

3 6 5 4

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by Brilliant Staff

Let $X, \ Y, \ Z$ be random variables over $\mathbb{Z}_{3}, \ \mathbb{Z}_{3}, \ \mathbb{Z}_{4},$ respectively, where $\mathbb{Z}_n$ denotes $\{1, 2, \dots, n\}.$ If $P_{X, Y, Z}(x, y, z) = \frac{xy}{144},$ what is the greatest integer less than or equal to $E[X + Y | Z]?$