How do I find the probability distribution of a dependent variable given the probability distributions of its independent variables?

I have two probability distribution functions, $$F$$ and $$G$$, describing quantities $$x$$ and $$y$$ respectively.

Both $$x$$ and $$y$$ are required to find quantity $$z$$ – let’s say $$z = x^2(1-cos(y))$$.

$$x$$ is defined over a range which we can call [x1, x2], while y is defined over [0,2π]. Both are continuous.

Given that I have $$F$$ and $$G$$, how can I find the probability distribution for $$z$$?

Thanks in advance!

Mathematics Asked by TempUserPerson on November 12, 2021

0 Answers

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