# Find PDF(X,Y) from PDF(X) and PDF(Y)

given that X and Y are not mutually exclusive, is there anyway to calculate PDF(X,Y) from PDF(X) and PDF(Y)? Following are a few plots made from the dataset.

In above image i have to find how PDF(11,56) is related to PDF(11), PDF(56). And in this case X and Y are not independent, but this might not always be true.

the dataset looks like this:

    diagnosis_ids   visit_days
0   (602,)      2
4   (3, 131)    2
5   (13,)       1
6   (442,)      3
7   (761,)      8
9   (28,)       2
10  (17,)       1
11  (13,)       1
12  (44,)       5
13  (9,)        2
14  (146,)      16
16  (9,)        2
17  (146, 336)  7
19  (88,)       5
20  (9,)        1

shape==> 75000 x 2
number of unique diagnosis_ids == 2000
visit_days == length of hospital stay in days.
max(len(diagnosis_ids)) = 6 (this is maximum len available in dataset, new entries can be longer than 6)


the final goal is to predict visit_days for a given combination of diagnosis_ids.

• What do you mean by mutually exclusive? By PDF you mean probability densities? Commented Jun 11, 2019 at 9:07
• yes PDF's are probability density functions and by mutually exclusive i mean any diagnosis_id can be combined with any other diagnosis_id, means a patient can have more than one diagnoses. Commented Jun 11, 2019 at 9:16
• This may help: math.chalmers.se/~rootzen/highdimensional/SSP4SE-appA.pdf if you are assuming normal distribution. Commented Jun 11, 2019 at 10:14