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12.4 Exercise 26

Avg difficulty 2.5

(See Exercise 16 from "Problems On Random Vectors and Joint Distributions", and Exercise 26 from "Problems on Mathematical Expectation"). fXY(t,u)=12t2uf_{X Y} \left(t , u\right) = 12 t^{2} u on the parallelogram with vertices

( - 1 , 0 ) , ( 0 , 0 ) , ( 1 , 1 ) , ( 0 , 1 ) \left(- 1 , 0\right) , \left(0 , 0\right) , \left(1 , 1\right) , \left(0 , 1\right)
E [ X ] = 2 5 , E [ Y ] = 11 15 , E [ X 2 ] = 2 5 E \left[X\right] = \frac{2}{5} , E \left[Y\right] = \frac{11}{15} , E \left[X^{2}\right] = \frac{2}{5}

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 26

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.