9.1.4. Properties of Expectation

Try these first

1. 1.

   Find E(10). What is it?

   Hint

   The expectation of a constant equals the constant itself.

2. 2.

   If E(X) = 4, find E(2X).

   Hint

   Use the linearity property.

3. 3.

   What is E(0)?

   • 0
   • 1
   • Undefined

   Hint

   Think about how constants behave.

4. 4.

   If X and Y are independent, does E(XY) = E(X) + E(Y)?

   • True
   • False

   Hint

   Recall the multiplicative property.

5. 5.

   Let X and Y be independent random variables with E(X) = 4 and Var(X) = 9. Compute E(X^2) using the properties learned.

   Hint

   Remember the formula for variance relates to expectation!

6. 6.

   Prove the multiplicative property of expectation for independent random variables using definitions.

   Hint

   Write out the definitions and express independence clearly.