Probability

Expected Value

Expected Value - Independent Variables

         

Let XX be a uniform random variable over {0,1,…,6},\{0, 1, \dots, 6\}, and YY a random variable over {0,1,…,4}\{0, 1, \dots, 4\} with P(Y=y)=y10.P(Y=y) = \frac{y}{10}. If XX and YY are independent, what is E[XY]? E[XY] ?

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

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

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

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

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