14.6.1. Expectation (Mean)

Try these first

1. 1.

   What is the expectation E[X] for a discrete random variable X with outcomes 1, 2, and 3 having probabilities 0.2, 0.5, and 0.3 respectively?

   Hint

   Multiply each outcome by its probability and sum the results.

2. 2.

   In a simple game, you can roll a die. What is the expected value of the roll?

   Hint

   Use the average of the outcomes of a fair die.

3. 3.

   What is the formula for expectation E[X] for discrete random variables?

   Hint

   Think of how averages are calculated.

4. 4.

   True or False: The expectation of a continuous random variable is obtained by a summation.

   • True
   • False

   Hint

   Remember the difference between discrete and continuous cases.

5. 5.

   Suppose X and Y are two independent random variables each with a mean of 3. Calculate E[X + 2Y].

   Hint

   Use the linearity of expectation property.

6. 6.

   Given the joint pdf f(x,y) = 6xy in the region [0,1] find E[XY].

   Hint

   Make sure to set up the correct double integral.