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handout_week6_c - Z is then found from f Z z = Z ∞-∞ f...

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Stochastic Signals and Systems Multiple Random Variables Virginia Tech Fall 2008 One Function of Two RVs: Method 2 Fix one of the two random variables, say Y , at a particular one of its possible values y . Then Z = g ( X , y ) is random only through its dependence on the single random variable X . We have a transformation from the random variable X to the random variable Z , in which y is now only a parameter that is held ﬁxed. We can therefore determine the conditional probability density function f Z ( z | y ) of Z , given Y = y . The conditional probability density function of Z is f Z ( z | y ) = f X ( x | y ) ± ± ± ± x z ± ± ± ± ± ± ± ± x = g - 1 ( x , y ) The probability density function of

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Unformatted text preview: Z is then found from f Z ( z ) = Z ∞-∞ f Z ( z | y ) f Y ( y ) dy . One Function of Two RVs: Method 2 Let Z = X / Y . Determine the cdf and pdf f Z ( z ) . One Function of Two RVs: Method 2 The random variables X and Y have the joint density f X , Y ( x , y ) = ± x / y ≤ x ≤ y ≤ 2 otherwise Find the density of the product Z = XY . One Function of Two RVs: Method 2 Let Z = X / ( X + Y ) . Determine f Z ( z ) given x > 0 and y > 0. Example Let Z = X 2 + Y 2 . Determine f Z ( z ) ....
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handout_week6_c - Z is then found from f Z z = Z ∞-∞ f...

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