[Term Entry] NumPy Random Module: .normal()

content/numpy/concepts/random-module/terms/normal/normal.md

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+---
+Title: '.normal()'
+Description: 'Generates random samples from a normal (Gaussian) distribution.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Numpy'
+  - 'Python'
+  - 'Random'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/computer-science'
+---
+
+The **`.normal()`** function from NumPy's `random` module generates random numbers drawn from a normal (Gaussian) distribution, which is a continuous, bell-shaped distribution commonly used in statistics and data science.
+
+## Syntax
+
+```pseudo
+numpy.random.normal(loc=0.0, scale=1.0, size=None)
+```
+
+**Parameters:**
+
+- `loc` (float or array_like of floats, optional): The mean ($\mu$) of the distribution. Default is `0.0`.
+- `scale` (float or array_like of floats, optional): The standard deviation ($\sigma$) of the distribution. Must be non-negative. Default is `1.0`.
+- `size` (int or tuple of ints, optional): The output shape. Specifies the number or shape of random samples to generate. If `None` (default), a single sample is returned.
+
+**Return value:**
+
+- `out` (ndarray or scalar): Random samples from the normal distribution.
+  - If `size` is `None`, returns a single float.
+  - If `size` is specified, returns a NumPy array of the given shape with samples drawn from the normal distribution.
+
+## Statistical Properties
+
+- Mean ($μ$) = `loc`
+- Variance ($σ^2$) = $\text{scale}^2$
+
+The Probability Density Function (PDF) of the normal distribution is:
+
+$$
+p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \ e^{-\frac{(x-\mu)^2}{2\sigma^2}}
+$$
+
+- $\mu$ is the mean (`loc`).
+- $\sigma$ is the standard deviation (`scale`).
+
+## Example
+
+This example generates two reproducible random samples from a normal distribution with `loc = 0` (mean) and `scale = 1` (standard deviation):
+
+```py
+import numpy as np
+np.random.seed(15)
+result = np.random.normal(loc=0, scale=1, size=2)
+print(result)
+```
+
+The output for this code will be:
+
+```shell
+[-0.44493578  0.22274619]
+```
+
+Here:
+
+- `np.random.seed(15)` ensures the same random numbers are generated every time the code runs.
+- `np.random.normal()` draws two samples from the standard normal distribution.
+
+## Codebyte Example
+
+This codebyte example generates a 2×3 array of normally distributed random numbers with `loc = 5` (mean) and `scale = 2` (standard deviation):
+
+```codebyte/python
+import numpy as np
+np.random.seed(42)
+result = np.random.normal(loc=5, scale=2, size=(2, 3))
+print(result)
+```
+
+- `np.random.seed(42)` sets the random seed for consistent results.
+- `size=(2, 3)` creates a 2D array with 2 rows and 3 columns of normally distributed samples.