Random variable generation in SciPy - Time & Space Complexity

Time Complexity: Random variable generation

O(n)

Understanding Time Complexity

When we generate random numbers using scipy, we want to know how the time to get these numbers changes as we ask for more.

We ask: How does the time grow when we generate more random values?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

from scipy.stats import norm

# Generate n random values from a normal distribution
def generate_random_values(n):
    samples = norm.rvs(size=n)
    return samples

values = generate_random_values(1000)

This code generates n random numbers from a normal distribution using scipy.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Generating each random number one by one internally.
• How many times: Exactly n times, once for each requested random value.

How Execution Grows With Input

As we ask for more random numbers, the time grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 10 random number generations
100	About 100 random number generations
1000	About 1000 random number generations

Pattern observation: Doubling the number of values roughly doubles the work done.

Final Time Complexity

Time Complexity: O(n)

This means the time to generate random numbers grows linearly with how many numbers you want.

Common Mistake

[X] Wrong: "Generating 1000 random numbers takes the same time as generating 10 because computers are fast."

[OK] Correct: Even though computers are fast, each random number requires work, so more numbers mean more time.

Interview Connect

Understanding how time grows with input size helps you explain performance clearly and shows you know how algorithms scale in real tasks.

Self-Check

"What if we generate random numbers in batches of 100 instead of all at once? How would the time complexity change?"