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12.4 Exercise 27

Avg difficulty 2.5

(See Exercise 17 from "Problems On Random Vectors and Joint Distributions", and Exercise 27 from "Problems on Mathematical Expectation"). $f_{X Y} \left(t , u\right) = \frac{24}{11} t u$ for $0 \leq t \leq 2$ , $0 \leq u \leq \min \left\{1 , 2 - t\right\}$ .

E \left[X\right] = \frac{52}{55} , E \left[Y\right] = \frac{32}{55} , E \left[X^{2}\right] = \frac{627}{605}

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 27

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