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8.3 Exercise 16

Avg difficulty 2.5

fXY(t,u)=12t2uf_{X Y} \left(t , u\right) = 12 t^{2} u on the parallelogram with vertices (-1,0),(0,0),(1,1),(0,1)\left(- 1 , 0\right) , \left(0 , 0\right) , \left(1 , 1\right) , \left(0 , 1\right)

P ( X ≤ 1 / 2 , Y > 0 ) , P ( X < 1 / 2 , Y ≤ 1 / 2 ) , P ( Y ≥ 1 / 2 ) P \left(X \leq 1 / 2 , Y > 0\right) , P \left(X < 1 / 2 , Y \leq 1 / 2\right) , P \left(Y \geq 1 / 2\right)

Pfeiffer, Applied Probability, 8.3 Problems On Random Vectors and Joint Distributions, exercise 16

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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.