14.2 Exercise 8 — Applied Probability

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

The regression line of Y on X is $u = \left(- 124 t + 368\right) / 431$

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{12}{11} t + I_{\left(1 , 2\right]} \left(t\right) \frac{12}{11} t \left(2 - t\right)^{2}

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 8

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