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12.4 Exercise 29

Avg difficulty 2.5

(See Exercise 21 from "Problems On Random Vectors and Joint Distributions", and Exercise 31 from "Problems on Mathematical Expectation"). fXY(t,u)=213(t+2u)f_{X Y} \left(t , u\right) = \frac{2}{13} \left(t + 2 u\right), for 0≤t≤20 \leq t \leq 2, 0≤u≤min{2t,3-t}0 \leq u \leq \min \left\{2 t , 3 - t\right\}.

E [ X ] = 16 13 , E [ Y ] = 11 12 , E [ X 2 ] = 2847 1690 E \left[X\right] = \frac{16}{13} , E \left[Y\right] = \frac{11}{12} , E \left[X^{2}\right] = \frac{2847}{1690}

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 29

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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.