7.6. Mean (Expected Value)

Try these first

1. 1.

   Define the Mean as it relates to a random variable.

   Hint

   Think about how we find averages in everyday life.

2. 2.

   What is the integral used to calculate the Mean?

   Hint

   Consider the formula that involves the PDF.

3. 3.

   What does the Expected Value of a random variable represent?

   • The highest possible value
   • The average outcome
   • Total sum of values

   Hint

   Consider how averages reflect typical outcomes.

4. 4.

   True or False: The Mean can also be referred to as the Expected Value.

   • True
   • False

   Hint

   Think about the definitions we've covered for the Mean.

5. 5.

   Determine the Mean of a normal distribution with a PDF of f(x) = (1/(σ√(2π))) * e^(-(x-μ)²/(2σ²)). How does the Mean relate to the center of this curve?

   Hint

   Consider how the properties of the normal distribution affect its Mean.

6. 6.

   Evaluate the impact on the Mean if the distribution is skewed to the right with a PDF skewed positively. What would happen?

   Hint

   Reflect on how skewed distributions behave compared to symmetric ones.