python - CDF of two continuous random variables from PDF function

Question

So let's say we have a random variable M and it's continuous. Its PDF function is (4x^3)/81 for 0≤x≤3 and 0 for outside of this interval. And let's say we also have another continuous random variable N that depends on M like N = M^2 + 3. How can I plot the joint CDF of M and N?

question from:https://stackoverflow.com/questions/65646794/cdf-of-two-continuous-random-variables-from-pdf-function

Answer 1

Stackoverflow won't let me type this joint CDF derivation in because it thinks it is improperly formatted code, but here is an image of it.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

m = np.linspace(0,3,100)
n = np.linspace(3,12,100)
m_mesh,n_mesh = np.meshgrid(m,n)
joint_cdf = np.minimum(m_mesh,np.sqrt(n_mesh-3))**4/81
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(m_mesh, n_mesh, joint_cdf, cmap=cm.coolwarm,linewidth=0, antialiased=False)