Trying to model the PDF of the number of API calls that a cloud service will receive based on three PDFs. Not sure if my approach is sound.

Question

I've got three arrays sampled from normal probability density functions (PDFs) representing the following:

• Number of users the app will see in a day
• Number of interactions with the application/user
• Number of API calls/interaction

The data are represented in three arrays of length 1000 each. I'm assuming each of the three PDFs are independent of one another. How do I go about combining them to get a PDF of the total number of API calls/day?

I know element wise multiplication is probably the wrong way to go about it. Would I use convolution to combine the PDFs?

Is there any literature I can read up on regarding how mathematical modeling based on probabilities works?