9.3-dars: Shartli ehtimollik

P(A | B) = P(A VA B) / P(B)          (P(B) > 0)

Ma'nosi: B ro'y berdi — dunyo B gacha "toraydi";
         shu tor dunyoda A ning ulushi.

Jadvalda (1000 tashrif):
                 xarid   xarid emas   jami
  savatcha         90        110       200
  savatchasiz      30        770       800
  jami            120        880      1000

  P(xarid)             = 120 / 1000 = 0.12
  P(xarid | savatcha)  =  90 / 200  = 0.45

P(A VA B) = P(A) × P(B | A) = P(B) × P(A | B)

Zanjir: P(A VA B VA C) = P(A) × P(B | A) × P(C | A VA B)

Voronka: tashrif → savatcha → to'lov → xarid
  P(savatcha) = 0.20, P(to'lov | savatcha) = 0.60, P(xarid | to'lov) = 0.75
  P(xarid) = 0.20 × 0.60 × 0.75 = 0.09

B1, B2, ..., Bk — S ni bo'laklarga ajratadi (kesishmaydi, birgalikda — hammasi)

P(A) = P(A | B1) × P(B1) + P(A | B2) × P(B2) + ... + P(A | Bk) × P(Bk)

Qurilma bo'yicha:
  P(xarid) = P(xarid | mobil) × P(mobil) + P(xarid | kompyuter) × P(kompyuter)
           = 0.11 × 0.85 + 0.16 × 0.15 = 0.1175

import pandas as pd

# P(xarid | mobil)
df[df["qurilma"] == "mobil"]["xarid"].mean()

# Hamma segment: P(xarid | qurilma)
df.groupby("qurilma")["xarid"].mean()

# Jadval
pd.crosstab(df["qurilma"], df["xarid"])                         # soni
pd.crosstab(df["qurilma"], df["xarid"], normalize="index")      # P(xarid | qurilma)
pd.crosstab(df["qurilma"], df["xarid"], normalize="columns")    # P(qurilma | xarid)

# Mustaqillik tekshiruvi
p_a = df["xarid"].mean()
p_a_b = df[df["savatcha"]]["xarid"].mean()      # p_a ga yaqinmi?

# To'liq ehtimollik
ulush = df["qurilma"].value_counts(normalize=True)
shartli = df.groupby("qurilma")["xarid"].mean()
(ulush * shartli).sum()                         # = df["xarid"].mean()
QOIDA: shart — qaysi tomonda? · normalize="index" = qator sharti · n ni ko'rsat

P(A | B) = P(A VA B) / P(B) — shart dunyoni toraytiradi
P(A | B) ≠ P(B | A) — aylantirish uchun Bayes (9.4)
Zanjir — P(A) × P(B | A) × ... (voronka)
Mustaqil — P(A | B) = P(A); kesishmaydi ≠ mustaqil
To'liq ehtimollik — segmentlarning vaznli o'rtachasi

"""Shartli ehtimollik: jadval va crosstab (real pandas)."""

import pandas as pd


def main() -> None:
    df = pd.DataFrame({
        "savatcha": [True] * 200 + [False] * 800,
        "xarid": [True] * 90 + [False] * 110 + [True] * 30 + [False] * 770,
    })

    print("=== 1. Jadval (soni) ===")
    print(pd.crosstab(df["savatcha"], df["xarid"], margins=True, margins_name="jami"))

    print("\n=== 2. Shartsiz va shartli ===")
    print(f"  P(xarid)            = {df['xarid'].mean():.2f}")
    print(f"  P(xarid | savatcha) = {df[df['savatcha']]['xarid'].mean():.2f}")
    print(f"  P(xarid | savatchasiz) = {df[~df['savatcha']]['xarid'].mean():.4f}")

    print("\n=== 3. Ta'rif bo'yicha ===")
    p_ab = (df["savatcha"] & df["xarid"]).mean()
    p_b = df["savatcha"].mean()
    print(f"  P(xarid VA savatcha) / P(savatcha) = {p_ab:.3f} / {p_b:.2f} = {p_ab / p_b:.2f}")
    print("  ⭐ Shart dunyoni toraytiradi (1000 → 200)")


if __name__ == "__main__":
    main()

=== 1. Jadval (soni) ===
xarid     False  True  jami
savatcha
False       770    30   800
True        110    90   200
jami        880   120  1000

=== 2. Shartsiz va shartli ===
  P(xarid)            = 0.12
  P(xarid | savatcha) = 0.45
  P(xarid | savatchasiz) = 0.0375

=== 3. Ta'rif bo'yicha ===
  P(xarid VA savatcha) / P(savatcha) = 0.090 / 0.20 = 0.45
  ⭐ Shart dunyoni toraytiradi (1000 → 200)

"""Shartni aylantirish xatosi: P(mobil | xarid) vs P(xarid | mobil) (real pandas/numpy)."""

import numpy as np
import pandas as pd


def main() -> None:
    rng = np.random.default_rng(0)
    n = 20_000
    qurilma = rng.choice(["mobil", "kompyuter"], n, p=[0.85, 0.15])
    p = np.where(qurilma == "mobil", 0.11, 0.16)
    df = pd.DataFrame({"qurilma": qurilma, "xarid": rng.random(n) < p})

    print("=== 1. Marketing o'qigan son: P(qurilma | xarid) ===")
    print(pd.crosstab(df["qurilma"], df["xarid"], normalize="columns")[True].round(2).to_dict())

    print("\n=== 2. Kerakli son: P(xarid | qurilma) ===")
    print(pd.crosstab(df["qurilma"], df["xarid"], normalize="index")[True].round(3).to_dict())

    print("\n=== 3. Xulosa ===")
    print("  xaridorlarning ko'pi mobil — chunki tashrifning ko'pi mobil")
    print("  kompyuter foydalanuvchisi ko'proq xarid qiladi")
    print("  ⭐ normalize='index' vs 'columns' — boshqa savol")


if __name__ == "__main__":
    main()

=== 1. Marketing o'qigan son: P(qurilma | xarid) ===
{'kompyuter': 0.2, 'mobil': 0.8}

=== 2. Kerakli son: P(xarid | qurilma) ===
{'kompyuter': 0.158, 'mobil': 0.113}

=== 3. Xulosa ===
  xaridorlarning ko'pi mobil — chunki tashrifning ko'pi mobil
  kompyuter foydalanuvchisi ko'proq xarid qiladi
  ⭐ normalize='index' vs 'columns' — boshqa savol

"""Sotuv voronkasi: zanjir qoidasi (real pandas/numpy)."""

import numpy as np
import pandas as pd


def main() -> None:
    rng = np.random.default_rng(1)
    n = 50_000
    savatcha = rng.random(n) < 0.20
    tolov = savatcha & (rng.random(n) < 0.60)
    xarid = tolov & (rng.random(n) < 0.75)
    df = pd.DataFrame({"savatcha": savatcha, "tolov": tolov, "xarid": xarid})

    print("=== 1. Bosqich konversiyalari (shartli) ===")
    p1 = df["savatcha"].mean()
    p2 = df[df["savatcha"]]["tolov"].mean()
    p3 = df[df["tolov"]]["xarid"].mean()
    print(f"  P(savatcha)            = {p1:.3f}")
    print(f"  P(to'lov | savatcha)   = {p2:.3f}")
    print(f"  P(xarid | to'lov)      = {p3:.3f}")

    print("\n=== 2. Zanjir ===")
    print(f"  ko'paytma: {p1 * p2 * p3:.4f}")
    print(f"  to'g'ridan: P(xarid) = {df['xarid'].mean():.4f}")

    print("\n=== 3. Eng zaif bosqich ===")
    bosqichlar = {"tashrif→savatcha": p1, "savatcha→to'lov": p2, "to'lov→xarid": p3}
    print(f"  {min(bosqichlar, key=bosqichlar.get)}")
    print("  ⭐ P(A VA B VA C) = P(A) × P(B|A) × P(C|A,B)")


if __name__ == "__main__":
    main()

=== 1. Bosqich konversiyalari (shartli) ===
  P(savatcha)            = 0.199
  P(to'lov | savatcha)   = 0.600
  P(xarid | to'lov)      = 0.750

=== 2. Zanjir ===
  ko'paytma: 0.0896
  to'g'ridan: P(xarid) = 0.0896

=== 3. Eng zaif bosqich ===
  tashrif→savatcha
  ⭐ P(A VA B VA C) = P(A) × P(B|A) × P(C|A,B)

"""Mustaqillik tekshiruvi va to'liq ehtimollik formulasi (real pandas/numpy)."""

import numpy as np
import pandas as pd


def main() -> None:
    rng = np.random.default_rng(2)
    n = 30_000
    df = pd.DataFrame({
        "qurilma": rng.choice(["mobil", "kompyuter"], n, p=[0.85, 0.15]),
        "hafta_kuni": rng.choice(["ish kuni", "dam olish"], n, p=[0.7, 0.3]),
    })
    df["xarid"] = rng.random(n) < np.where(df["qurilma"] == "mobil", 0.11, 0.16)

    print("=== 1. Mustaqillik: xarid va hafta kuni ===")
    print(f"  P(xarid) = {df['xarid'].mean():.3f}")
    print(f"  P(xarid | dam olish) = {df[df['hafta_kuni'] == 'dam olish']['xarid'].mean():.3f}  (yaqin — mustaqil)")

    print("\n=== 2. Bog'liqlik: xarid va qurilma ===")
    print(df.groupby("qurilma")["xarid"].mean().round(3).to_dict())

    print("\n=== 3. To'liq ehtimollik ===")
    ulush = df["qurilma"].value_counts(normalize=True)
    shartli = df.groupby("qurilma")["xarid"].mean()
    print(f"  sum(P(xarid|q) × P(q)) = {(ulush * shartli).sum():.4f}")
    print(f"  P(xarid)               = {df['xarid'].mean():.4f}")

    print("\n=== 4. Tarkib o'zgarsa (mobil 95%) ===")
    yangi = 0.95 * shartli["mobil"] + 0.05 * shartli["kompyuter"]
    print(f"  umumiy konversiya: {yangi:.4f}  (segmentlar o'zgarmasa ham tushdi)")
    print("  ⭐ Umumiy = segmentlarning vaznli o'rtachasi")


if __name__ == "__main__":
    main()

=== 1. Mustaqillik: xarid va hafta kuni ===
  P(xarid) = 0.115
  P(xarid | dam olish) = 0.115  (yaqin — mustaqil)

=== 2. Bog'liqlik: xarid va qurilma ===
{'kompyuter': 0.137, 'mobil': 0.111}

=== 3. To'liq ehtimollik ===
  sum(P(xarid|q) × P(q)) = 0.1153
  P(xarid)               = 0.1153

=== 4. Tarkib o'zgarsa (mobil 95%) ===
  umumiy konversiya: 0.1127  (segmentlar o'zgarmasa ham tushdi)
  ⭐ Umumiy = segmentlarning vaznli o'rtachasi

pd.crosstab(df["qurilma"], df["xarid"], normalize="columns")   # P(q | xarid)  # ⚠️
pd.crosstab(df["qurilma"], df["xarid"], normalize="index")     # P(xarid | q)  # ✅

p = (df["savatcha"] & df["xarid"]).sum() / len(df)    # bu P(A VA B)  # ⚠️
p = (df["savatcha"] & df["xarid"]).sum() / df["savatcha"].sum()      # ✅

df.groupby("shahar")["xarid"].mean()                               # ⚠️
df.groupby("shahar")["xarid"].agg(["mean", "count"])               # ✅

p_ikkalasi = p_a * p_b            # bog'liq bo'lsa xato              # ⚠️
p_ikkalasi = (df["a"] & df["b"]).mean()   # ma'lumotdan              # ✅

umumiy = p1 + p2 + p3                                              # ⚠️
umumiy = p1 * p2 * p3                                              # ✅

# "konversiya 12% dan 11% ga tushdi — sayt yomonlashdi"           # ⚠️
# segment bo'yicha ham ko'ring (groupby) — tarkib o'zgarganmi?     # ✅

df[df["shahar"] == "Nukus"]["xarid"].mean()   # 0 qator → NaN       # ⚠️
# avval: (df["shahar"] == "Nukus").sum() > 0                        # ✅

1.  # P(A | B) formulasi?
2.  # P(A | B) = P(B | A)?
3.  # jadvalda 90/200 — qaysi shart?
4.  # mustaqillik ta'rifi?
5.  # kesishmaydi = mustaqil?
6.  # voronka: 0.2 × 0.5 × 0.5?
7.  # normalize="index"?
8.  # normalize="columns"?
9.  # to'liq ehtimollik nima?
10. # tarkib o'zgarsa umumiy konversiya?
11. # 1-karta tuz, 2-si ham (qaytarmasdan)?
12. # klassifikator nimani baholaydi?

1.  pd.crosstab(df["q"], df["xarid"], normalize="columns")   # P(xarid | q) kerak

2.  p = (df["a"] & df["b"]).sum() / len(df)   # P(a | b) kerak

3.  umumiy = p1 + p2 + p3   # voronka

4.  p_ikkalasi = p_a * p_b   # a va b bog'liq

5.  df.groupby("shahar")["xarid"].mean()   # n yo'q