Demand for your company’s product is influenced by two factors: economic conditions for the year (good, fair or poor) and the intensity of market competition (intense or moderate). Company analysts estimate a likelihood of 30% that economic conditions will be good, a 50% likelihood that they will be fair, and a 20% likelihood they will be poor.
It is estimated that if economic conditions are good, there is an 80% probability that market competition will be intense (and so a 20% chance it will be only moderate). If economic conditions are only fair, there is a 50% chance that competition will be intense (and a 50% chance it will be moderate). Finally, if economic conditions are poor, there is only a 10% chance that competition will be intense (and a 90% chance it will be moderate).
The company has a basic demand level of 5000 units, but its analysts estimate that good economic conditions will add 2000 units to this total, while fair economic conditions will add 1500. (Poor conditions will add nothing to basic demand.) In addition, moderate competition can be expected to add an extra 1000 units, while intense competition will subtract 1000 units.
Using company demand as your random variable and x to represent values of the random variable,
a. List the possible x values.
b. Show the full probability distribution.
c. Compute the expected demand.