generate uniformly distributed 3D coordinates between 0 and 1 using python

I would like to write a python script to generate a uniformly distributed 3D coordinates (e.g., x, y, z) where x, y, and z are float numbers between 0 and 1. For the moment, z can be fixed, thus what I need is a uniform distributed points in a 2D (x-y) plane. I have written a script to do this job and checked both x, and y are uniform numbers. However, I am not sure if these points are uniformly distributed in (x-y) plane.

My code is

1 import matplotlib.pyplot as plt
2 import random
3 import numpy as np
4 import csv
5 nk1=300
6 nk2=300
7 nk3=10
8 kx=[]
9 ky=[]
10 kz=[]
11 for i in range(nk1):
12     for j in range(nk2):
13         for k in range(nk3):
14             xkg1=random.random()
15             xkg2=random.random()
16             xkg3 = float(k)/nk3
17             kx.append(xkg1)
18             ky.append(xkg2)
19             kz.append(xkg3)
20 kx=np.array(kx)
21 count, bins, ignored = plt.hist(kx, normed=True)
22 plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
23 plt.show()

The plot shows both "kx", and "ky" are uniformly distributed numbers, however, how can I make sure that x-y are uniformly distributed in the 2D plane?