# Beklenen Değer ve Varyans

Canonical: https://manyspace.aporia.systems/tr/topics/expectation-variance-mth-prob-204
Updated: 2026-10-13

Matematik · Probability · MTH-PROB-204

- Zorluk: 3 / 5
- Önem: 5 / 5
- Çalışma süresi: 4–7.5 sa

moments, LOTUS, properties, covariance, correlation

## Neden önemli

The mathematics of uncertainty; foundation for statistics, ML, finance, quantum mechanics and stochastic processes.

## Nerede kullanılır

Risk assessment, A/B testing, machine learning models, financial derivatives, statistical mechanics, hiring decisions.

## Öğrendiğini nasıl anlarsın

Solve ≥10 representative problems with ≥80% adjusted accuracy.

## Önce neye ihtiyacın var

- [Rastgele Değişkenler ve Dağılımlar](https://manyspace.aporia.systems/tr/topics/rastgele-degiskenler-ve-dagilimlar-mth-prob-200) (gerekli)
- [Kısmi İntegrasyon](https://manyspace.aporia.systems/tr/topics/kismi-integrasyon-mth-calc2-140) (gerekli)
- [Sayma İlkeleri](https://manyspace.aporia.systems/tr/topics/sayma-ilkeleri-mth-disc-112) (yardımcı)

## Neyi açar

- [Büyük Sayılar Yasası](https://manyspace.aporia.systems/tr/topics/buyuk-sayilar-yasasi-mth-prob-209)
- [Nokta Tahmini](https://manyspace.aporia.systems/tr/topics/nokta-tahmini-mth-stats-215)
- [Nash Dengesi](https://manyspace.aporia.systems/tr/topics/nash-dengesi-mth-game-350)
- [Utility and Rational Decisions](https://manyspace.aporia.systems/tr/topics/utility-and-rational-decisions-aiml-aif-009)
- [CAC ve LTV](https://manyspace.aporia.systems/tr/topics/cac-ve-ltv-ent-growth-103)
- [Bias-Variance Trade-off](https://manyspace.aporia.systems/tr/topics/bias-variance-trade-off-aiml-gen-003)

## Kaynaklar

- An Introduction to Probability Theory (Vol 1) — William Feller
- Introduction to Probability (Blitzstein & Hwang) — Blitzstein & Hwang
- Introduction to Probability (Blitzstein & Hwang) — Blitzstein & Hwang