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8.3 Exercise 22

Avg difficulty 2.5

fXY(t,u)=I[0,1](t)38(t2+2u)+I(1,2](t)914t2u2f_{X Y} \left(t , u\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{3}{8} \left(t^{2} + 2 u\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{9}{14} t^{2} u^{2} for 0≤u≤10 \leq u \leq 1.

P ( 1 / 2 ≤ X ≤ 3 / 2 , Y ≤ 1 / 2 ) P \left(1 / 2 \leq X \leq 3 / 2 , Y \leq 1 / 2\right)

Pfeiffer, Applied Probability, 8.3 Problems On Random Vectors and Joint Distributions, exercise 22

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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.