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12.4 Exercise 23

Avg difficulty 2.5

(See Exercise 10 from "Problems On Random Vectors and Joint Distributions", and Exercise 20 from "Problems on Mathematical Expectation"). $f_{X Y} \left(t , u\right) = 1$ for $0 \leq t \leq 1$ , $0 \leq u \leq 2 \left(1 - t\right)$ .

E \left[X\right] = \frac{1}{3} , E \left[X^{2}\right] = \frac{1}{6} , E \left[Y\right] = \frac{2}{3}

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 23

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