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Asked Dec 6, 2019
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A joint probability density function is given by f(x,y) = x+y, 0<=x,y<=1. Find conditional expectation of y, given x = 0.5.

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Expert Answer

Step 1

A joint probability density function is given by,

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f (x, y) = x+ y,0<r,y<1

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Step 2

The marginal density function of x is calculated as follows:

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S.(x) = [ /(x.v)dv =[(x+y)dy = xy +. Ix =x + Зx? ||

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Step 3

The conditional probability density f...

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S, (x,v) 5. (x = 0.5) Syx-s( \ x = 0.5) = Xy x+ y 3.x? 2 Ix=0.5 2(0.5+ y) 3x 0.5 = 2.6667(y+0.5)

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