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Q11Section A (Section A)11 of 60

Conditional probability given X from a joint density

Let (X,Y)(X,Y) have the joint probability density function

f(x,y)={12y2e−x,0<y<x<∞, 0,otherwise.f(x,y)=\begin{cases}\frac12y^2e^{-x}, & 0<y<x<\infty,\ 0, & \text{otherwise.}\end{cases}

Then P(Y<1∣X=3)P(Y<1|X=3) equals

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