chapter_4/poker_test_three_digit.ipynb

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    "each random number is of `three digits`. The following combination are possible: <br>\n",
    "(a) All three of different kind  <br>\n",
    "(b) One pair  <br>\n",
    "(c) All three of same kind <br>\n",
    "\n",
    "\n",
    "The probability of occurrence of combination (a), that is All three of different kind, <br>\n",
    "P (a) = 0.9 x .8 = 0.72  <br>\n",
    "The probability having one pair is,  <br>\n",
    "P (b) =(3/2) *.1 × .9  = 0.27 <br>\n",
    "The probability of having All three of same kind is, <br>\n",
    "P(c)= .1 x .1 = 0.01 <br>\n",
    "\n"
   ]
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    "import random\n",
    "import scipy.stats as stats\n",
    "\n",
    "\n",
    "# def generate_random_number():\n",
    "#     return random.randint(100, 999)\n",
    "\n",
    "# # Generate a sequence of 10,000 random five-digit numbers\n",
    "# random_numbers = [generate_random_number() for _ in range(10000)]\n",
    "\n",
    "\n",
    "observed_frequencies = {\n",
    "    'All three of different kind': 680,\n",
    "    'One pair': 289,\n",
    "    'All three of same kind': 31\n",
    "}\n",
    "\n",
    "\n",
    "total_numbers = sum(observed_frequencies.values())\n",
    "\n",
    "# if random number not given in question\n",
    "# total_numbers = len(random_numbers)\n",
    "# for num in random_numbers:\n",
    "#     digits = [int(d) for d in str(num)]\n",
    "#     digit_counts = [digits.count(d) for d in set(digits)]\n",
    "\n",
    "#     if len(set(digits)) == 3:\n",
    "#         observed_frequencies['All three of different kind'] += 1\n",
    "#     elif 2 in digit_counts:\n",
    "#         observed_frequencies['One pair'] += 1\n",
    "#     elif all(count == 3 for count in digit_counts):\n",
    "#         observed_frequencies['All three of same kind'] += 1\n",
    "\n",
    "\n",
    "print(\"Observed frequencies:\")\n",
    "for combination, count in observed_frequencies.items():\n",
    "    print(f\"{combination}: {count} ({count / total_numbers * 100:.2f}%)\")\n",
    "\n",
    "expected_frequencies = {\n",
    "    'All three of different kind': total_numbers * 0.72,\n",
    "    'One pair': total_numbers * 0.27,\n",
    "    'All three of same kind': total_numbers * 0.01\n",
    "}\n",
    "\n",
    "\n",
    "print(\"===\")\n",
    "print(expected_frequencies)\n",
    "print(\"===\")\n",
    "\n",
    "\n",
    "chi_square = 0\n",
    "for combination in observed_frequencies:\n",
    "    observed = observed_frequencies[combination]\n",
    "    expected = expected_frequencies[combination]\n",
    "    chi_square += (observed - expected) ** 2 / expected\n",
    "\n",
    "print(\"Chi-square statistic:\", chi_square)\n",
    "\n",
    "\n",
    "# Compare chi_square value with critical chi-square value at desired significance level\n",
    "# Degrees of freedom for the chi-square test\n",
    "df = len(observed_frequencies) - 1\n",
    "\n",
    "# Significance level (alpha)\n",
    "alpha = 0.05\n",
    "\n",
    "# Critical chi-square value\n",
    "critical_chi_square = stats.chi2.ppf(1 - alpha, df)\n",
    "\n",
    "if chi_square > critical_chi_square:\n",
    "    print(\"Reject the null hypothesis. The random numbers are not independent.\")\n",
    "else:\n",
    "    print(\"Not reject the null hypothesis. The random numbers are independent.\")\n",
    "\n",
    "\n"
   ]
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