Investment Analysis - Probability

Question

Bob, the proprietor of Midway  Lumber, bases his projections for the annual revenues of the company on the performance of the housing market.  He rates the performance of the market as very strong, strong, normal, weak or very weak.  For the next year, Bob estimates that the probabilities for these outcomes are .18,  .27,  .42,  .10, and .03, respectively.  He also thinks that the revenues corresponding to these outcomes are $20,  $18.8,  $16.2 and $12 million, respectively.  What is Bob's expected revenue for next year?

Answer 1

To find the expected revenue, you multiply the amount of revenue by the probability of that revenue occurring, and then sum these amounts over all possible outcomes.  As a formula this is written  

 

E(X) = ∑ x*P(x)  

 

You have listed 5 probabilities (0.18, 0.27, 0.42, 0.10 and 0.03) and they sum to 1, as they should to cover the entire sample space.  But you have only listed 4 revenue amounts ($20, $18.8, $16.2 and $12).  If the 5th revenue amount is 0 and corresponds to the 0.03 probability then  

 

E(X) = 20*0.18 + 18.8*0.27 + 16.2*0.42 + 12*0.10 + 0*0.03

       = 3.6 + 5.076 + 6.804 + 1.2 + 0

       = $16.68 million  

 

If you have a different value for the 5th revenue amount you can plug it in to the equation to get a different answer.