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Properties of Expectation Calculator

Online expectation properties: E(aX+b)=aE(X)+b, with no independence required.

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E(aX+b)=aE(X)+b
Coefficient
Constant

📖 Tutorial | Expectation Properties

1. Definition
Expectation properties: E(c)=c, E(aX+b)=aE(X)+b, E(X+Y)=E(X)+E(Y).
2. Formula & Notation
a,bCoefficient, constant
3. Properties & Laws
  • Linearity;
  • No independence needed;
  • E(c)=c;
  • Sum of expectations.
4. Steps
  1. Enter the distribution and a,b;
  2. Click "Verify";
  3. Or click "Load Example".
5. Worked Examples
Example: E(X)=2.3,a=2,b=3: E(2X+3)=7.6.
6. Common Pitfalls
Multiply a, add b;
No independence;
Include b.

❓ FAQ | Expectation Properties

Linearity?
aE+b.
E(c)?
c.
Sum?
Sum of expectations.
Independence?
Not needed.
Example?
7.6.
a=0?
E(b)=b.