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8.3 Exercise 20

Avg difficulty 2.5

fXY(t,u)=12227(3t+2tu)f_{X Y} \left(t , u\right) = \frac{12}{227} \left(3 t + 2 t u\right) for 0≤t≤20 \leq t \leq 2, 0≤u≤min{1+t,2}0 \leq u \leq \min \left\{1 + t , 2\right\}

P ( X ≤ 1 / 2 , Y ≤ 3 / 2 ) , P ( X ≤ 1 . 5 , Y > 1 ) , P ( Y < X ) P \left(X \leq 1 / 2 , Y \leq 3 / 2\right) , P \left(X \leq 1 . 5 , Y > 1\right) , P \left(Y < X\right)

Pfeiffer, Applied Probability, 8.3 Problems On Random Vectors and Joint Distributions, exercise 20

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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.