1.10 Independent Random Variables and Conditioning When There Is Dependence

Random variables X1, …, Xk are said to be mutually independent if

FX1,,Xk(x1,,xk)=i=1kFXi(xi)for allx1,,xk.

si231_e  (8a)

Equivalently, for mutually independent rv’s,

fX1,,Xk(x1,,xk)=i=1kfXi(xi)for allx1,,xk,

si232_e  (8b)

holds for their joint pdf or joint pmf. The conditional pmf or pdf of Xr+1, …, Xk given (X1, …, Xr) = (x1, …, xr) when fX1,,Xr(x1,,xr)>0si233_e is

f(Xr+1,

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