Expected Value

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 $E[XY] ?$

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

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 $c?$

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

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 $E[ (X-3)( Y- 3)( Z- 2)( W- 3) ] ?$

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Expected Value - Independent Variables

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