Expected Earnings

Probability · Axiom Academy

How to evaluate job offers when your income isn't guaranteed You've just graduated and received two job offers. Both are in sales, but they have very different compensation structures: At first glance, Job A seems safer. But is it better? Let's use expected value to make an informed decision. For Job B, your total monthly earnings depend on how much you sell. The company provided data from their current sales team showing the probability distribution of monthly sales: Notice that your earnings are a discrete random variable because they can only take specific values ( 3,000, 4,000, 5,000, 6,000, or 7,000), and each outcome has a known probability. Expected Value: Your Average Earnings The expected value (or expected earnings) tells you what you'd earn on average per month if you worked this job for a long time. It's calculated by multiplying each possible earning by its probability, then summing: Let's calculate the expected value for Job B: Based on expected value alone, which job pays more on average? Expected value tells us the long-run average, but it doesn't tell the whole story. Job B has higher variability (also called variance or risk). Adjust the slider to see how different months might play out: Most common outcome - you're earning 500 more than Job A Key insight: With Job B, there's a 15% chance you'll earn only 3,000 (less than Job A), but there's also a 20% chance you'll earn 6,000 or more (significantly more than Job A).

This is the written version of the interactive lesson above. See the full Probability course.