Solutions Probability

Suppose that {{f}_{Y|X}}(y|x)={ 1 x

Question: Suppose that

fY∣X(y∣x)={1              x<y<x+10              otherwise{{f}_{Y|X}}\left( y|x \right)=\left\{ \begin{aligned} & 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<y<x+1 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.

and X has a Uniform (0,1) distribution

(a) Find E(Y)E\left( Y \right)

(b) Find fX∣Y(x∣y){{f}_{X|Y}}\left( x|y \right)

(c) Find Pr⁡(X+Y<1)\Pr \left( X+Y<1 \right)

Solution:

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