Back to 14.2 Problems on Conditional Expectation, Regression

14.2 Exercise 5

Avg difficulty 2.5

(See Exercise 13 from " Problems On Random Vectors and Joint Distributions", Exercise 23 from "Problems on Mathematical Expectation", and Exercise 24 from "Problems on Variance, Covariance, Linear Regression"). fXY(t,u)=18(t+u)f_{X Y} \left(t , u\right) = \frac{1}{8} \left(t + u\right) for 0≤t≤20 \leq t \leq 2, 0≤u≤20 \leq u \leq 2.

The regression line of Y on X is u=-t/11+35/33u = - t / 11 + 35 / 33.

f X ( t ) = 1 4 ( t + 1 ) , 0 ≤ t ≤ 2 f_{X} \left(t\right) = \frac{1}{4} \left(t + 1\right) , 0 \leq t \leq 2

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 5

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.