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Joint Density Function • The joint density function of two random variables X and Y, denoted f X,Y (x, y) gives the density of probability per unit area at the point (x, y). • B Y X dy dx y x f B Y X P , , ,

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Joint Density Function. The joint density function of two random variables X and Y , denoted f X,Y ( x , y ) gives the density of probability per unit area at the point ( x , y ). Marginal Densities. Joint Density for Independent RVs. - PowerPoint PPT Presentation

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Page 1: Joint Density Function

Joint Density Function

• The joint density function of two random variables X and Y, denoted fX,Y(x, y) gives the density of probability per unit area at the point (x, y).

• B

YX dydxyxfBYXP ,, ,

Page 2: Joint Density Function

Marginal Densities

dxyxfyf

dyyxfxf

YXY

YXX

,

,

,

,

Page 3: Joint Density Function

Joint Density for Independent RVs

• Random variables X and Y are independent if and only if the joint density of X and Y is the product of the two marginal densities:

yxyfxfyxf YXYX ,,,


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