Back to 14.2 Problems on Conditional Expectation, Regression

14.2 Exercise 4

Avg difficulty 2.5

(See Exercise 10 from "Problems On Random Vectors and Joint Distributions", Exercise 20 from "Problems on Mathematical Expectation", and Exercise 23 from "Problems on Variance, Covariance, Linear Regression"). fXY(t,u)=1f_{X Y} \left(t , u\right) = 1 for 0≤t≤10 \leq t \leq 1, 0≤u≤2(1-t)0 \leq u \leq 2 \left(1 - t\right).

The regression line of Y on X is u=1-tu = 1 - t.

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

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 4

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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.