Expected Value

Expected Value is a statistical concept that represents the predicted value of a random variable. It’s essentially a weighted average of all possible values, where the weights are the probabilities of each value occurring.

Process

  1. Identify all possible outcomes: Determine all the potential results of an event.
  2. Assign probabilities: Determine the probability of each outcome occurring.
  3. Calculate the product: Multiply each outcome by its probability.
  4. Sum the products: Add up all the results from step 3.

Formula:

Expected Value (EV) = Σ (Outcome * Probability)

Applications:

  • Gambling: To analyze the fairness of games.
  • Investments: To evaluate the potential return of an investment.
  • Insurance: To determine premiums.
  • Decision making: To weigh the potential outcomes of different choices.

While expected value provides a useful tool for analysis, it doesn’t guarantee the actual outcome. It’s a long-term average and doesn’t predict what will happen in a single instance.