Added PMF problem

Author: Jeet009

.DS_Store

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+## Problem
+
+Given a list of integer samples drawn from a discrete distribution, implement a function to compute the empirical Probability Mass Function (PMF). The function should return a list of `(value, probability)` pairs sorted by the value in ascending order. If the input is empty, return an empty list.

old_repo/Problems/.DS_Store

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+{
+  "input": "samples = [1, 2, 2, 3, 3, 3]",
+  "output": "[(1, 0.16666666666666666), (2, 0.3333333333333333), (3, 0.5)]",
+  "reasoning": "Counts are {1:1, 2:2, 3:3} over 6 samples, so probabilities are 1/6, 2/6, and 3/6 respectively, returned sorted by value."
+}

questions/182_PMF/description.md

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+
+# Learn Section
+
+# Probability Mass Function (PMF) — Simple Explanation
+
+A **probability mass function (PMF)** describes how probabilities are assigned to the possible outcomes of a **discrete random variable**.
+
+- It tells you the chance of each specific outcome.  
+- Each probability is non-negative.  
+- The total of all probabilities adds up to 1.
+
+## Estimating from data
+If the true probabilities are unknown, you can estimate them with an **empirical PMF**:
+- Count how often each outcome appears.  
+- Divide by the total number of observations.  
+
+## Example
+Observed sequence: `1, 2, 2, 3, 3, 3` (6 outcomes total)
+- “1” appears once → estimated probability = 1/6  
+- “2” appears twice → estimated probability = 2/6 = 1/3  
+- “3” appears three times → estimated probability = 3/6 = 1/2  
+
+
+    

questions/182_PMF/example.json

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+{
+  "id": "182",
+  "title": "Empirical Probability Mass Function (PMF)",
+  "difficulty": "easy",
+  "category": "Probability & Statistics",
+  "video": "",
+  "likes": "0",
+  "dislikes": "0",
+  "contributor": [
+    {
+      "profile_link": "https://github.com/jeetmukherjee",
+      "name": "jeetmukherjee"
+    }
+  ]
+}

questions/182_PMF/learn.md

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+from collections import Counter
+
+def empirical_pmf(samples):
+    """
+    Given an iterable of integer samples, return a list of (value, probability)
+    pairs sorted by value ascending.
+    """
+    samples = list(samples)
+    if not samples:
+        return []
+    total = len(samples)
+    cnt = Counter(samples)
+    result = [(k, cnt[k] / total) for k in sorted(cnt.keys())]
+    return result

questions/182_PMF/meta.json

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+def empirical_pmf(samples):
+    """
+    Given an iterable of integer samples, return a list of (value, probability)
+    pairs sorted by value ascending.
+    """
+    # TODO: Implement the function
+    pass

questions/182_PMF/solution.py

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+[
+  {
+    "test": "print(empirical_pmf([1, 2, 2, 3, 3, 3]))",
+    "expected_output": "[(1, 0.16666666666666666), (2, 0.3333333333333333), (3, 0.5)]"
+  },
+  {
+    "test": "print(empirical_pmf([5, 5, 5, 5]))",
+    "expected_output": "[(5, 1.0)]"
+  },
+  {
+    "test": "print(empirical_pmf([]))",
+    "expected_output": "[]"
+  },
+  {
+    "test": "print(empirical_pmf([0, 0, 1, 1, 1, 2]))",
+    "expected_output": "[(0, 0.3333333333333333), (1, 0.5), (2, 0.16666666666666666)]"
+  }
+]