9.1.5. Variance and Relation to Expectation

Try these first

1. 1.

   What is the expectation of a fair 6-sided die?

   Hint

   Add the outcomes and divide by the number of faces.

2. 2.

   How do you define variance?

   Hint

   Think about how far each value is from the average.

3. 3.

   What is the formula for variance?

   • E[X²] - (E[X])²
   • E[X] - E[X²]
   • E[X²] + E[X]

   Hint

   Recall the definitions of expectation and variance.

4. 4.

   True or False: Variance measures how concentrated the mean is.

   • True
   • False

   Hint

   Think about what variance represents.

5. 5.

   A random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Calculate Var(X).

   Hint

   Use the probabilities to find E(X) and E(X²) first.

6. 6.

   Explain how variance plays a role in the context of stochastic PDEs and provide a specific example.

   Hint

   Link variance with real-life applications in PDEs!