Understanding change of probability density function or proability mass function when "Marginal probability distribution" rule

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Nobody actually tell me this simple question so I ask here.

For below formula, probability distribution marginalizing, does P(X) and P(X, Y) share same form of PDF or PMF? I assume the PDF or PMF will not be same, but I think it should have some kind of set of PDF or PMF and it works inside it.

Am I right?

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