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Expected Value (EV), also called mathematical expectation, is the probability-weighted average of all possible outcomes of a random variable. It represents the long-run average result if an experiment is repeated many times. EV is the cornerstone of decision theory, financial modelling, insurance, and gambling strategy.

Công thức

E(X) = Σ xᵢ × P(xᵢ) for all outcomes i
E
Σ xᵢ × P(xᵢ) for all outcomes i — Σ xᵢ × P(xᵢ) for all outcomes i
X
Σ xᵢ × P(xᵢ) for all outcomes i — Σ xᵢ × P(xᵢ) for all outcomes i
P
P value — Variable used in the calculation

Hướng dẫn từng bước

  1. 1E(X) = Σ xᵢ × P(xᵢ) for all outcomes i
  2. 2All probabilities must sum to 1
  3. 3Variance σ² = Σ P(xᵢ) × (xᵢ − E(X))²
  4. 4Standard deviation σ = √Variance — measures spread around the mean
  5. 5A positive EV game is profitable in the long run; negative EV is a loss

Ví dụ có lời giải

đầu vào
Roll a fair die — win £6 if you roll 6, lose £1 otherwise
Kết quả
EV = 6×(1/6) + (−1)×(5/6) = +£0.17/roll
Positive EV — play!
đầu vào
UK lottery — £2 ticket, jackpot £5M, odds 1 in 45M
Kết quả
EV ≈ −£1.89 per ticket
Very negative EV

Câu hỏi thường gặp

What is Expected Value?

Expected Value (EV), also called mathematical expectation, is the probability-weighted average of all possible outcomes of a random variable. It represents the long-run average result if an experiment is repeated many times

How accurate is the Expected Value calculator?

The calculator uses the standard published formula for expected value. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Expected Value calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Expected Value calculator use?

The core formula is: E(X) = Σ xᵢ × P(xᵢ) for all outcomes i. Each step in the calculation is shown so you can verify the result manually.

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