9.1.3. Expectation for Continuous Random Variables

Try these first

1. 1.

   What is the expectation of a random variable X uniformly distributed between 0 and 10?

   Hint

   Use the formula for uniform distribution.

2. 2.

   How does expectation relate to the average value?

   Hint

   Consider the definition of mean.

3. 3.

   What is the expectation E(X) for a continuous variable with pdf f(x)?

   Hint

   Think about the integral definition related to area under a curve.

4. 4.

   True or False: The expectation of a random variable is always a value that the variable can take.

   • True
   • False

   Hint

   Consider how averages can sometimes lie outside the original set, like for a uniform distribution.

5. 5.

   Consider a continuous random variable X with pdf f(x) = 2x for 0 <= x <= 1. Calculate the expectation E(X) and interpret the result.

   Hint

   Set up the integral carefully and bear in mind the function shape.

6. 6.

   A stock's price follows a normal distribution with a mean of $50 and standard deviation of$10. Calculate the expected price after 1 year assuming the same conditions hold.

   Hint

   Consider why the mean value remains constant.