Example showing densities of random variables in conditional joint probability space.

conditional.py

from sympy.stats import *
from sympy import Tuple, Eq, simplify, Symbol, pprint
X = Normal('x', 3, 4)
Y = Normal('y', 5, 6)
Z = Normal('z', 0, 1)

# X, Y, and Z given that Z+Y == X
XX, YY, ZZ = given(Tuple(X, Y, Z), Eq(Z+Y, X))

w = Symbol('w')

pprint(simplify(density(XX)(w)))

#                 2                
#             53⋅w    191⋅w   36481
#           - ───── + ───── - ─────
#   ______     1184    592    62752
# ╲╱ 3922 ⋅ℯ                       
# ─────────────────────────────────
#                   ___            
#             296⋅╲╱ π