Expected Value

Front

What is Expected Value?

Back

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.

Front

How do you calculate Expected Value?

Back

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

Front

What is the Expected Value of a random variable with outcomes 1, 2, and 3 with probabilities 0.3, 0.43, and 0.27 respectively?

Back

EV = (1 * 0.3) + (2 * 0.43) + (3 * 0.27) = 1.97.

Front

If the Expected Value is positive, what does it indicate?

Back

A positive Expected Value indicates that, on average, you are expected to win or gain from the situation.

Front

What does a negative Expected Value signify?

Back

A negative Expected Value indicates that, on average, you are expected to lose or incur a cost from the situation.

Front

What is a fair game in terms of Expected Value?

Back

A fair game is one where the Expected Value is zero, meaning neither the player nor the house has an advantage.

Front

In a coin flip game where heads wins $3 and tails loses $4, what is the Expected Value?

Back

EV = (3 * 0.5) + (-4 * 0.5) = -$0.50.

Front

What is the Expected Value of rolling a fair die with a payout of $3 for rolling a 2 or 4?

Back

EV = (3 * 1/6) + (0 * 4/6) - $1 = $0.50.

Front

What is the significance of Return on Investment (ROI) in relation to Expected Value?

Back

ROI measures the gain or loss generated relative to the investment cost, and a higher ROI often correlates with a higher Expected Value.

Front

What is the Expected Value of a game where you pay $1 to play and have a 1/3 chance to win $3?

Back

EV = (3 * 1/3) - 1 = $0.