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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 - Independent Variables

Let $X$ be a uniform random variable over $\{0, 1, \dots, 6\},$ and $Y$ a random variable over $\{0, 1, \dots, 4\}$ with $P(Y=y) = \frac{y}{10}.$ If $X$ and $Y$ are independent, what is $E[XY] ?$

7 12 9 10

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If $X$ and $Y$ are independent random variables such that $E[X] = 12$ and $E[Y] = 17 ,$ what is $E[ (X-4)( Y- 5) ] ?$

120 132 96 108

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by Brilliant Staff

If $X$ and $Y$ are independent random variables such that $E[X] = 11,$ $E[Y] = 20 ,$ and $E[ (X-c)( Y- 9) ] = 88,$ what is $c?$

4 2 3 5

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If $X$ and $Y$ are independent random variables such that $E[X] = 15$ and $E[ (X-4)( Y- 9) ] = 99,$ what is $E[Y] ?$

21 16 18 19

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If $X, \ Y, \ Z,$ and $W$ are independent random variables such that $E[X] = 6,$ $E[Y] = 5 ,$ $E[Z] = 4 ,$ and $E[W] = 11 ,$ what is $E[ (X-3)( Y- 3)( Z- 2)( W- 3) ] ?$

288 672 480 96

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by Brilliant Staff

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