Expected Value

Expected Value (EV) is a calculated average of all possible outcomes of a random variable, weighted by their probabilities. It represents the long-term average if the experiment were repeated many times.

To calculate Expected Value, multiply each possible outcome by its probability and sum all these products: EV = Σ (Outcome × Probability).

A game is considered 'fair' if the expected value of the game is zero, meaning that the average outcome is neither a gain nor a loss over time.

To find the expected value of a lottery ticket, calculate the probability of winning multiplied by the prize amount, then subtract the cost of the ticket.

EV = (1/6 * 3) + (4/6 * 0) = 0.5, which means the expected value is $0.50.

EV = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 5 + 6 + 3 = 14.

The expected number of cars for a randomly chosen American household is 1.75.

The mean of a probability distribution is the expected value, representing the center of the distribution and the average outcome.

Risk in decision-making can be assessed by comparing the expected value of different choices, helping to identify options with higher potential returns versus losses.

A fair game has an expected value of zero, meaning that the average winnings equal the average losses over time.