New file numpy.random.geometric

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

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+---
+Title: '.geometric()'
+Description: 'Genereates random samples from the specified geometric distribution.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+  - 'Data Visualization'
+Tags:
+  - 'Data'
+  - 'Numpy'
+  - 'Random'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/computer-science'
+---
+
+The **`.geometric()`** function in `numpy.random` returns random samples from a geometric distribution based on a given probability of success, with the option to control the number of samples through the `size` parameter.
+
+## Syntax
+
+```pseudo
+numpy.random.geometric(p, size=None)
+```
+
+**Parameters:**
+
+- `p` (float or array_like): Probability of success for each trial. Must be in the range (0, 1].
+- `size` (int or tuple of ints, optional): Output shape. If `None`, a single value is returned.
+
+**Return value:**
+
+Returns random samples drawn from the geometric distribution, representing the number of trials until the first success.
+
+The probability mass function of geometric distribution is:
+
+$$
+f(k) = (1 - p)^{k - 1} \ p
+$$
+
+`p` in this case is the success probability of an individual trial.
+
+## Example
+
+The following code returns 10 random samples from a geometric distribution with the probability of success set to 0.35:
+
+```py
+import numpy as np
+
+#  Setting the seed ensures reproducible results
+np.random.seed(42)
+
+results = np.random.geometric(p=0.35, size=10)
+print(results)
+```
+
+The output of this code would be:
+
+```shell
+[2 7 4 3 1 1 1 5 3 3]
+```
+
+## Codebyte Example
+
+This Codebyte simulates 100 coin flips with an unfair coin (35% chance of Heads), then counts how many trials resulted in a success on the first attempt:
+
+```codebyte/python
+import numpy as np
+
+# Set the seed for reproduceability
+np.random.seed(33)
+
+# Simulate 100 trials
+results = np.random.geometric(p=0.35, size=100)
+
+# How many trials succeeded on the first attempt?
+print((results == 1).sum())
+```
+
+Here:
+
+- `p=0.35`: Probability of success (e.g., the coin landing on Heads).
+- `size=100`: Generates 100 random samples.
+- `np.random.geometric(p, size)`: Returns the number of trials needed to get the first success.
+
+This example demonstrates how geometric distributions can model binary outcome processes like coin tosses where the goal is to measure how many attempts are needed to succeed once.