exercise:210c85d599

Let [math]X[/math] and [math]Y[/math] be continuous random variables with joint density function

[[math]] f(x,y) = \begin{cases} 24xy, \,\, 0 \lt x \lt 1 \,\, \textrm{and} \,\, 0 \lt y \lt 1-x \\ 0, \, \textrm{Otherwise.} \end{cases} [[/math]]

Calculate [math] \operatorname{P}[Y \lt X | X = 1/3][/math]

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Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.