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Given two random variables x and y. Their PDFs P(x) and P(y) are known. However, if we do not assume the independence between x and y, how can we represent the Cumulative Distribution Function F(xy) (yes, x multiplied by y).

I am not familiar with probability theory, and I have attempted to write some double integral begin with $\textrm{p(xy<=Z)=p(y<=Z/x)}$ but I am still very confused...

Could anyone please give me some hints? highly appreciate it!

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    $\begingroup$ The problem as you have stated it is impossible. You cannot derive the cdf of xy from the two marginal distributions. You would instead need to know the joint distribution. $\endgroup$
    – Gordon Smyth
    Commented Mar 26, 2022 at 8:40
  • $\begingroup$ Thanks for your attention and reply! Could you please tell me the mathematical equation to compute P(xy) given P(x,y)? $\endgroup$
    – Richardson
    Commented Mar 26, 2022 at 8:49
  • $\begingroup$ It depends on how you represent the joint distribution. Are you working with a specific example? (If not, maybe you should be...) $\endgroup$
    – whuber ♦
    Commented Mar 26, 2022 at 14:34

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