Let X, Y. and Z be three random variables with joint PDF
Chapter , Problem 29(choose chapter or problem)
Let X, Y. and Z be three random variables with joint PDF /x.y.z . Show the multiplication rule: /x.Y.z (x, Y, z) = /xlY,z (x I y, z)/Ylz (Y I z)/z(z). Solution. We have, using the definition of conditional density, and / ( I ) - /x,Y,z(x, y, z) x I y,Z x Y, z - / ( ) Y.Z Y,Z , /Y,z (y, z) = /YIZ (Y I z)/z (z). Combining these two relations, we obtain the multiplication rule.
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