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12.4 Exercise 25

Avg difficulty 2.5

(See Exercise 15 from "Problems On Random Vectors and Joint Distributions", and Exercise 25 from "Problems on Mathematical Expectation"). $f_{X Y} \left(t , u\right) = \frac{3}{88} \left(2 t + 3 u^{2}\right)$ for $0 \leq t \leq 2$ , $0 \leq u \leq 1 + t$ .

E \left[X\right] = \frac{313}{220} , E \left[Y\right] = \frac{1429}{880} , E \left[X^{2}\right] = \frac{49}{22}

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 25

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