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Statistics

Expected Value Calculator

Expected value of two outcomes. Free online Expected Value Calculator. Calculate expected value online — fast, accurate, mobile-friendly, no signup needed.

E(X)
25

Derivation

  1. ├── 01Givenp1 = 0.5, v1 = 100, v2 = -50
  2. ├── 02Formulat × e.v1+(1-t) × e.v2
  3. ├── 03Substitutet × e.100+(1-t) × e.-50
  4. └── 04Compute E(X)25
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§01What is

Understanding the Expected Value Calculator

The Expected Value Calculator computes E(X) from 3 inputs: p₁, value 1, value 2. Expected value of two outcomes.

Statistics is how we make sense of noisy real-world data. Whether you’re analysing survey results, sports scores, or business metrics, a statistics calculator gives you the exact formula-based answer so you can focus on the interpretation. The Expected Value Calculator sits in that toolkit — it expected value of two outcomes. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t × e.v1+(1-t) × e.v2

Where

p1
P₁
v1
Value 1
v2
Value 2
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: P₁ = 0.5, Value 1 = 100, Value 2 = -50.

  1. 01Start by noting the input — P₁: 0.5.
  2. 02Start by noting the input — Value 1: 100.
  3. 03Start by noting the input — Value 2: -50.
  4. 04Substitute these values into the formula: t × e.v1+(1-t) × e.v2
  5. 05Compute E(X): the calculator returns 25.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Expected Value Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

P₁ halved

p1 = 0.25 (from 0.5)

Keep every other input at its default and halve the p₁. See how e(x) responds.

  1. 01New P₁: 0.25
  2. 02Baseline E(X): 25
  3. 03New E(X): -12.5
  4. 04E(X) decreases by 150% → use this sensitivity to plan for real-world variation.
02 · PATTERN

P₁ doubled

p1 = 1 (from 0.5)

Keep every other input at its default and double the p₁. See how e(x) responds.

  1. 01New P₁: 1
  2. 02Baseline E(X): 25
  3. 03New E(X): 100
  4. 04E(X) increases by 300% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Value 1 halved

v1 = 50 (from 100)

Keep every other input at its default and halve the value 1. See how e(x) responds.

  1. 01New Value 1: 50
  2. 02Baseline E(X): 25
  3. 03New E(X): 0
  4. 04E(X) decreases by 100% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Value 1 doubled

v1 = 200 (from 100)

Keep every other input at its default and double the value 1. See how e(x) responds.

  1. 01New Value 1: 200
  2. 02Baseline E(X): 25
  3. 03New E(X): 75
  4. 04E(X) increases by 200% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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