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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Discrete Mathematics

Expected Value

Concept Quizzes

Definition
Properties
Linearity of Expectation
Independent Variables
Expected Values

Challenge Quizzes

Level 2
Level 3
Level 4
Level 5

Expected Value - Properties

If \(E[3X+Y] = 11\) and \(E[X] = 2,\) what is \( E[Y]?\)

5 11 7 9

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If \(E[4X ] = 16 ,\) what is \( E[X] ?\)

9 5 4 8

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If \(E[3X+9Y] = 6\) and \(E[3X+Y] = 5,\) what is \( E[X+Y]?\)

\[{ \frac{15}{32}} \] \[{ \frac{7}{4}} \] \[{ \frac{22}{15}} \] \[{ \frac{7}{3}} \]

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If \( E[X] = 3 ,\) what is \(E[3X + 1 ]?\)

11 21 10 20

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If \(E[X] = 4, E[Y] = 4 ,\) what is \(E[4X+3Y]?\)

57 29 28 56

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