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I have two random variables whose PDF are parameterized by an unknown constant as follows:

P(A;d) P(B;d)

apparently, these two are not independent, so to find P(A+B;d) one cannot use convolution.

1- Do you have any idea how to procede?

2- is my statement about independence correct?

Thanks

Pioneer83
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1 Answers1

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Correct, you can no longer use convolution.

If your random variables are now dependent, then in order to know the PDF of their sum you need to know their joint PDF [$P(A,B;d)$ according to your notation].

Once you know this, look at this question:

How to add two dependent random variables?

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Amir
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