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October 26th, 2017, 07:04 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Interpretation of Conditional Distribution of a Function of a Random Variable
I know how to find the conditional distribution of two random variables, say X and Y, given their probability density function: f(Y  X=x) = f(x, y) / f(x) However, suppose I want to find the conditional distribution of a function of a random variable. For example: Does f(Y/(1x)  X=x) = f(x, y/(1x)) / f(x) ? If not, what does f(Y/(1x)  X=x) mean? The forward slash represents division. 
October 26th, 2017, 08:42 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,039 Thanks: 1063 
not quite.. to find the density you'd have to find the expression for the CDF given $X=x$ and then differentiate. It's unlikely the form of the PDF will look like $\dfrac{f(Y)}{1x}$ 

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conditional, distribution, function, interpretation, random, variable 
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