14.2 Exercise 9 — Applied Probability

(See Exercise 18 from " Problems On Random Vectors and Joint Distributions", Exercise 28 from "Problems on Mathematical Expectation", and Exercise 28 from "Problems on Variance, Covariance, Linear Regression"). $f_{X Y} \left(t , u\right) = \frac{3}{23} \left(t + 2 u\right)$ for $0 \leq t \leq 2$ , $0 \leq u \leq \max \left\{2 - t , t\right\}$ .

The regression line of Y on X is $u = 1 . 0561 t - 0 . 2603$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{6}{23} \left(2 - t\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{23} t^{2}

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 9

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