9.1.6. Expectation in Applications of PDEs

Try these first

1. 1.

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

   Hint

   Use the average of the outcomes from 1 to 6.

2. 2.

   If a coin is flipped, what is the expected number of heads in 3 flips?

   Hint

   Consider the probability of heads in each flip.

3. 3.

   What is the expected value of a fair 6-sided die?

   • 2
   • 3
   • 3.5
   • 4

   Hint

   Think about the sum of the possible results divided by the number of outcomes.

4. 4.

   True or False: The expectation of the sum of random variables equals the sum of their expectations.

   • True
   • False

   Hint

   Consider how averages aggregate.

5. 5.

   Given a PDF f(x) = 2x for 0 < x < 1, calculate E(X).

   Hint

   Use integration to find the average under the probability density function.

6. 6.

   Explain how stochastic PDEs arise in real-world scenarios. Provide a detailed example.

   Hint

   Connect physical systems and randomness in your explanation.