Generate uniform distributed random samples of real number within the range of [0,1]

Here is one way to generate uniform distributed random samples of real numbers within the range of [0,1]:

1. Use a random number generator that generates random numbers uniformly distributed within the range of [0,1]. This could be a built-in function in a programming language or a physical random number generator.

2. Call the random number generator multiple times to generate as many random samples as needed.

3. Each time a random number is generated, it is a sample from the uniform distribution within the range of [0,1]. Repeat this process to generate as many samples as needed.

For example, in Python, you can use the random module to generate uniform random numbers within the range of [0,1]:

import random

# Generate a single random sample
x = random.uniform(0, 1)
print(x)

# Generate 10 random samples
samples = [random.uniform(0, 1) for _ in range(10)]
print(samples)

This will output something like:

0.7945034273800846
[0.17406314360864247, 0.89403787495006, 0.8126840177356334, 0.5043613429359189, 0.15490938936444088, 0.8119324604423194, 0.06450851469828522, 0.9315235346673164, 0.8943672216118687, 0.04022757022471001]