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October 26th, 2017, 08:04 PM   #1
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Exclamation 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/(1-x) | X=x) = f(x, y/(1-x)) / f(x) ? If not, what does f(Y/(1-x) | X=x) mean?

The forward slash represents division.
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October 26th, 2017, 09:42 PM   #2
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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 $\dfrac{f(Y)}{1-x}$
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