# Probability

This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2.

Are X and Y independent?

Find fX(x). Express your answers in terms of x using standard notation .

If 0<x<1,

If 1<x<2,

Find fY|X(y∣0.5).

If 0<y<1/2,

Find fX|Y(x∣0.5).

If 1/2<x<1,

If 1<x<3/2,

Let R=XY and let A be the event {X<0.5}. Evaluate E[R∣A].

E[R∣A]= ??

1. 👍 0
2. 👎 0
3. 👁 655
1. 1. Are X and Y independent? NO

2. Find fX(x). Express your answers in terms of x using standard notation .

If 0<x<1,

fX(x)= x/2

If 1<x<2,

fX(x)= -3*x/2+3

Find fY|X(y∣0.5).

If 0<y<1/2,

fY|X(y∣0.5)= 2

3. Find fX|Y(x∣0.5).

If 1/2<x<1,

fX|Y(x∣0.5)= 0.5

If 1<x<3/2,

fX|Y(x∣0.5)= 1.5

Let R=XY and let A be the event {X<0.5}. Evaluate E[R∣A].

E[R∣A]= 0.0625

1. 👍 1
2. 👎 0

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