What is going wrong? You convolved the PDF of one variable with the CDF of the other.

np.convolve(a=pdf, v=cdf)

Problem: Convolving a PDF with a CDF does not yield a valid PDF or CDF. The convolution operation for summing random variables specifically requires convolving the PDFs of the variables.

Incorrect Formula:

𝐹𝑋+𝑌(𝑎)=(𝐹𝑋∗𝑔)(a)

How to Correct It:

Convolve the PDFs of X and Y to get the PDF of Z= X +Y and then Integrate the resulting PDF to obtain the CDF of Z.