the probability distribution of dependent variables

There are three variables, X3 is a function of X1 and X2, X2 also depends on X1.The dependency relationship is shown as the following graph.

In specific, X3= f(X1, x2) and X2=g(X1). Therefore, X3=f(X1, g(X1)). If the probabilistic distribution of X1 is known, how to get the probabilistic distribution of X3.

Topic probabilistic-programming mcmc bayesian probability statistics

Category Data Science

1
answered at

You need to tell us what the distribution of x1 is and what f and g function are exactly? When f and g are simple, we can usually solve this analytically. But when the function is complex, this kind of problems are typically approximated by Monte Carlo simulation.

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