Numpy - numpy.random.randn()

What does numpy.random.randn() do?

 

ChatGPT said:

numpy.random.randn() is a function in NumPy that generates random numbers from a standard normal distribution — also known as the Gaussian distribution with:

• mean (μ) = 0

• standard deviation (σ) = 1

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🔹 Syntax

numpy.random.randn(d0, d1, d2, ...)

• Each argument (d0, d1, …) specifies the dimension (shape) of the output array.

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🔹 Examples

1. Generate a single random number

import numpy as np
x = np.random.randn()
print(x)

Output example:

0.12573022

(Each time you run it, the value will be different.)

2. Generate a 1D array of 5 numbers

np.random.randn(5)

Example output:

array([-0.672, 0.856, -1.12, 0.307, 0.98])

3. Generate a 2×3 matrix

np.random.randn(2, 3)

Example output:

array([[ 0.32, -0.75, 1.22], [-1.03, 0.43, -0.21]])

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🔹 Key Points

• Values come from the standard normal distribution N(0,1)N(0, 1)N(0,1).

• To scale or shift the distribution, you can apply:

  mean = 10
  std = 2
  x = std * np.random.randn(5) + mean

  → Generates numbers from N(10,22)N(10, 2^2)N(10,22).

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✅ In short:
np.random.randn() → draws samples from the standard normal distribution, and the arguments define the array’s shape.

 

You said:

mean = 10
std = 2
x = std * np.random.randn(5) + mean

You said above code Generates numbers from N(10, 2^2). But I think it generates numbers from N(10, 2). Were you right or am I right?

 

ChatGPT said:

Excellent question — and you’re actually right to ask this 👏

Let’s clear this up carefully.

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🧠 The key point:

In a normal distribution N(μ,σ²),

• μ = mean

• σ² = variance

• σ = standard deviation

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📘 What np.random.randn() gives

np.random.randn() generates samples from N(0,1), meaning:

• mean = 0

• standard deviation = 1

• variance = 1² = 1

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📗 What your code does

mean = 10
std = 2
x = std * np.random.randn(5) + mean

This transforms the distribution as:

➡ Therefore:

• mean: 10

• standard deviation: 2
  

• variance: 2²=4

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✅ Correct interpretation:

The resulting distribution is

That is: mean = 10, standard deviation = 2, variance = 4.

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🧩 So to summarize:

Expression	Meaning
N(10, 2)	mean = 10, variance = 2
N(10, 2²)	mean = 10, standard deviation = 2

Most conventions (including in NumPy and statistics) use N(mean, variance) — so N(10, 2²) is the correct way to write it.

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✅ Final Answer:
I was right — it generates numbers from N(10, 2²) (mean = 10, standard deviation = 2, variance = 4).
Your intuition was good — you just mixed up variance and standard deviation notation.